## Merle, Frank

Compute Distance To:
 Author ID: merle.frank Published as: Merle, Frank; Merle, F.; Merle, Franck more...less Homepage: https://www.ihes.fr/en/professeur/frank-merle-2/ External Links: MGP · Wikidata · ResearchGate · Math-Net.Ru · dblp · IdRef · theses.fr
 Documents Indexed: 159 Publications since 1987 4 Contributions as Editor Co-Authors: 33 Co-Authors with 137 Joint Publications 1,175 Co-Co-Authors
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### Co-Authors

 26 single-authored 35 Martel, Yvan 28 Raphael, Pierre 24 Kenig, Carlos Eduardo 23 Zaag, Hatem 20 Duyckaerts, Thomas 9 Szeftel, Jérémie 6 Rodnianski, Igor 5 Peletier, Lambertus Adrianus 4 Berestycki, Henri 4 Hilhorst, Danielle 4 Mimura, Masayasu 4 Pakdaman, Khashayar 3 Brézis, Haïm 3 Collot, Charles 3 Matano, Hiroshi 2 Balabane, Mikhael 2 Cazenave, Thierry 2 Côte, Raphaël 2 Douady, Adrien 2 Fibich, Gadi 2 Filippas, Stathis 2 Glangetas, Léo 2 Golse, François 2 Rivière, Tristan 2 Tsai, Tai-Peng 2 Tsutsumi, Yoshio 2 Vega, Luis 1 Antonini, Christophe 1 Fermanian-Kammerer, Clotilde 1 Mizumachi, Tetsu 1 Nakanishi, Kenji 1 Roudenko, Svetlana 1 Serrin, James
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### Serials

 16 Communications in Mathematical Physics 9 IMRN. International Mathematics Research Notices 9 Comptes Rendus de l’Académie des Sciences. Série I 7 Communications on Pure and Applied Mathematics 7 Geometric and Functional Analysis. GAFA 7 Séminaire Équations aux Dérivées Partielles 6 Archive for Rational Mechanics and Analysis 6 Duke Mathematical Journal 6 Inventiones Mathematicae 5 American Journal of Mathematics 5 Journal of Functional Analysis 5 Annals of Mathematics. Second Series 4 Mathematische Annalen 4 Journal of the American Mathematical Society 4 Discrete and Continuous Dynamical Systems 4 Journal of the European Mathematical Society (JEMS) 4 Networks and Heterogeneous Media 3 Journal of Differential Equations 3 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 3 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 3 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V 2 Nonlinearity 2 Acta Mathematica 2 Indiana University Mathematics Journal 2 Transactions of the American Mathematical Society 2 Physica D 2 Comptes Rendus. Mathématique. Académie des Sciences, Paris 2 Cambridge Journal of Mathematics 2 Séminaire Laurent Schwartz. EDP et Applications 1 Journal d’Analyse Mathématique 1 Journal of Mathematical Physics 1 Russian Mathematical Surveys 1 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 1 Proceedings of the American Mathematical Society 1 Chinese Annals of Mathematics. Series B 1 Revista Matemática Iberoamericana 1 The Journal of Geometric Analysis 1 Communications in Partial Differential Equations 1 Journal de Mathématiques Pures et Appliquées. Neuvième Série 1 Annales de l’Institut Henri Poincaré. Physique Théorique 1 Journées Équations aux Dérivées Partielles (Saint-Jean-de-Monts) 1 Methods and Applications of Analysis 1 Bulletin des Sciences Mathématiques 1 Documenta Mathematica 1 Revista Matemática Complutense 1 Communications on Pure and Applied Analysis 1 Journal of Hyperbolic Differential Equations 1 IMRP. International Mathematics Research Papers
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### Fields

 161 Partial differential equations (35-XX) 22 Dynamical systems and ergodic theory (37-XX) 8 Fluid mechanics (76-XX) 3 General and overarching topics; collections (00-XX) 3 Ordinary differential equations (34-XX) 3 Quantum theory (81-XX) 2 History and biography (01-XX) 1 Operator theory (47-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Optics, electromagnetic theory (78-XX)

### Citations contained in zbMATH Open

138 Publications have been cited 5,267 times in 2,008 Documents Cited by Year
Uniform estimates and blow-up behavior for solutions of $$-\Delta{} u =V(x) e^ u$$ in two dimensions. Zbl 0746.35006
Brézis, Haïm; Merle, Frank
1991
Global well-posedness, scattering and blow-up for the energy-critical, focusing, nonlinear Schrödinger equation in the radial case. Zbl 1115.35125
Kenig, Carlos E.; Merle, Frank
2006
Global well-posedness, scattering and blow-up for the energy-critical focusing non-linear wave equation. Zbl 1183.35202
Kenig, Carlos E.; Merle, Frank
2008
The blow-up dynamic and upper bound on the blow-up rate for critical nonlinear Schrödinger equation. Zbl 1185.35263
Merle, Frank; Raphaël, Pierre
2005
Determination of blow-up solutions with minimal mass for nonlinear Schrödinger equations with critical power. Zbl 0808.35141
Merle, F.
1993
On universality of blow up profile for $$L^2$$ critical nonlinear Schrödinger equation. Zbl 1067.35110
Merle, Frank; Raphaël, Pierre
2004
Construction of solutions with exactly k blow-up points for the Schrödinger equation with critical nonlinearity. Zbl 0707.35021
Merle, Frank
1990
Stability and asymptotic stability for subcritical gKdV equations. Zbl 1017.35098
Martel, Yvan; Merle, Frank; Tsai, Tai-Peng
2002
Compactness at blow-up time for $$L^2$$ solutions of the critical nonlinear Schrödinger equation in 2D. Zbl 0913.35126
Merle, F.; Vega, L.
1998
On a sharp lower bound on the blow-up rate for the $$L^2$$ critical nonlinear Schrödinger equation. Zbl 1075.35077
Merle, Frank; Raphaël, Pierre
2006
Universality of blow-up profile for small radial type II blow-up solutions of the energy-critical wave equation. Zbl 1230.35067
Duyckaerts, Thomas; Kenig, Carlos; Merle, Frank
2011
L$${}^ 2$$ concentration of blow-up solutions for the nonlinear Schrödinger equation with critical power nonlinearity. Zbl 0722.35047
Merle, Frank; Tsutsumi, Yoshio
1990
On nonexistence of type II blowup for a supercritical nonlinear heat equation. Zbl 1112.35098
Matano, Hiroshi; Merle, Frank
2004
Sharp upper bound on the blow-up rate for the critical nonlinear Schrödinger equation. Zbl 1061.35135
Merle, Frank; Raphaël, Pierre
2003
Classification of the radial solutions of the focusing, energy-critical wave equation. Zbl 1308.35143
Duyckaerts, Thomas; Kenig, Carlos; Merle, Frank
2013
Profiles and quantization of the blow up mass for critical nonlinear Schrödinger equation. Zbl 1062.35137
Merle, Frank; Raphaël, Pierre
2005
Asymptotic stability of solitons for subcritical generalized KdV equations. Zbl 0981.35073
Martel, Yvan; Merle, Frank
2001
Stability of the blow-up profile for equations of the type $$u_ t=\Delta u+| u| ^{p-1}u$$. Zbl 0872.35049
Merle, Frank; Zaag, Hatem
1997
Existence of blow-up solutions in the energy space for the critical generalized KdV equation. Zbl 0970.35128
Merle, Frank
2001
A Liouville theorem for the critical generalized Korteweg-de Vries equation. Zbl 0963.37058
Martel, Yvan; Merle, Frank
2000
Blow up in finite time and dynamics of blow up solutions for the $$L^2$$-critical generalized KdV equation. Zbl 0996.35064
Martel, Yvan; Merle, Frank
2002
Instability of solitons for the critical generalized Korteweg-de Vries equation. Zbl 0985.35071
Martel, Y.; Merle, F.
2001
Dynamic of threshold solutions for energy-critical NLS. Zbl 1232.35150
Duyckaerts, Thomas; Merle, Frank
2009
Asymptotic stability of solitons of the subcritical gKdV equations revisited. Zbl 1064.35171
Martel, Yvan; Merle, Frank
2005
Multi solitary waves for nonlinear Schrödinger equations. Zbl 1133.35093
Martel, Yvan; Merle, Frank
2006
Stability in $$H^1$$ of the sum of $$K$$ solitary waves for some nonlinear Schrödinger equations. Zbl 1099.35134
Martel, Yvan; Merle, Frank; Tsai, Tai-Peng
2006
Scattering for $$\dot {H}^{1/2}$$ bounded solutions to the cubic, defocusing NLS in 3 dimensions. Zbl 1188.35180
Kenig, Carlos E.; Merle, Frank
2010
Classification of type I and type II behaviors for a supercritical nonlinear heat equation. Zbl 1178.35084
Matano, Hiroshi; Merle, Frank
2009
Profiles of bounded radial solutions of the focusing, energy-critical wave equation. Zbl 1258.35148
Duyckaerts, Thomas; Kenig, Carlos; Merle, Frank
2012
Dynamics of threshold solutions for energy-critical wave equation. Zbl 1159.35043
Duyckaerts, Thomas; Merle, Frank
2008
Construction of multi-soliton solutions for the $$L^2$$-supercritical gKdV and NLS equations. Zbl 1273.35234
Côte, Raphaël; Martel, Yvan; Merle, Frank
2011
Existence of stationary states for nonlinear Dirac equations. Zbl 0696.35154
Merle, F.
1988
Stability of blow-up profile and lower bounds for blow-up rate for the critical generalized KdV equation. Zbl 1005.35081
Martel, Yvan; Merle, Frank
2002
Quantization effects for $$-\Delta u=u(1-| u|^ 2)$$ in $$\mathbb{R}^ 2$$. Zbl 0809.35019
Brézis, Haïm; Merle, Frank; Rivière, Tristan
1994
Universality of the blow-up profile for small type II blow-up solutions of the energy-critical wave equation: the nonradial case. Zbl 1282.35088
Duyckaerts, Thomas; Kenig, Carlos E.; Merle, Frank
2012
Solution of a nonlinear heat equation with arbitrarily given blow-up points. Zbl 0785.35012
Merle, Frank
1992
Blowup dynamics for smooth data equivariant solutions to the critical Schrödinger map problem. Zbl 1326.35052
Merle, Frank; Raphaël, Pierre; Rodnianski, Igor
2013
A Liouville theorem for vector-valued nonlinear heat equations and applications. Zbl 0939.35086
Merle, Frank; Zaag, Hatem
2000
Determination of the blow-up rate for the semilinear wave equation. Zbl 1052.35043
Merle, Frank; Zaag, Hatem
2003
Nondispersive radial solutions to energy supercritical non-linear wave equations, with applications. Zbl 1241.35136
Kenig, Carlos E.; Merle, Frank
2011
On uniqueness and continuation properties after blow-up time of self- similar solutions of nonlinear Schrödinger equation with critical exponent and critical mass. Zbl 0767.35084
Merle, Frank
1992
Existence of excited states for a nonlinear Dirac field. Zbl 0696.35158
1988
Determination of the blow-up rate for a critical semilinear wave equation. Zbl 1136.35055
Merle, Frank; Zaag, Hatem
2005
Existence and universality of the blow-up profile for the semilinear wave equation in one space dimension. Zbl 1133.35070
Merle, Frank; Zaag, Hatem
2007
Existence and classification of characteristic points at blow-up for a semilinear wave equation in one space dimension. Zbl 1252.35204
Merle, Frank; Zaag, Hatem
2012
Optimal estimates for blowup rate and behavior for nonlinear heat equations. Zbl 0899.35044
Merle, Frank; Zaag, Hatem
1998
Asymptotic stability of solitons of the gKdV equations with general nonlinearity. Zbl 1153.35068
Martel, Yvan; Merle, Frank
2008
Existence of self-similar blow-up solutions for Zakharov equation in dimension two. I. Zbl 0808.35137
Glangetas, L.; Merle, F.
1994
Nonexistence of minimal blow-up solutions of equations $$iu_ t = -\Delta u - k(x)| u|^{4/N} u$$ in $$\mathbb{R}^ N$$. Zbl 0846.35129
Merle, Franck
1996
Blow up for the critical generalized Korteweg-de Vries equation. I: Dynamics near the soliton. Zbl 1301.35137
Martel, Yvan; Merle, Frank; Raphaël, Pierre
2014
Openness of the set of non-characteristic points and regularity of the blow-up curve for the 1 D semilinear wave equation. Zbl 1159.35046
Merle, Frank; Zaag, Hatem
2008
Concentration properties of blow-up solutions and instability results for Zakharov equation in dimension two. II. Zbl 0808.35138
Glangetas, L.; Merle, F.
1994
Scattering for radial, bounded solutions of focusing supercritical wave equations. Zbl 1310.35171
Duyckaerts, Thomas; Kenig, Carlos; Merle, Frank
2014
Soliton resolution along a sequence of times for the focusing energy critical wave equation. Zbl 1391.35276
Duyckaerts, Thomas; Jia, Hao; Kenig, Carlos; Merle, Frank
2017
On the stability of the notion of non-characteristic point and blow-up profile for semilinear wave equations. Zbl 1315.35134
Merle, Frank; Zaag, Hatem
2015
Refined uniform estimates at blow-up and applications for nonlinear heat equations. Zbl 0926.35024
Merle, F.; Zaag, H.
1998
Description of two soliton collision for the quartic gKdV equation. Zbl 1300.37045
Martel, Yvan; Merle, Frank
2011
Blow up for the critical gKdV equation. III: Exotic regimes. Zbl 1331.35307
Martel, Yvan; Merle, Frank; Raphaël, Pierre
2015
Threshold and generic type I behaviors for a supercritical nonlinear heat equation. Zbl 1223.35088
Matano, Hiroshi; Merle, Frank
2011
$$L^2$$ stability of solitons for KdV equation. Zbl 1022.35061
Merle, F.; Vega, L.
2003
Proof of a spectral property related to the singularity formation for the $$L^{2}$$ critical nonlinear Schrödinger equation. Zbl 1100.35097
Fibich, Gadi; Merle, Frank; Raphaël, Pierre
2006
Blow up for the critical gKdV equation. II: Minimal mass dynamics. Zbl 1326.35320
Martel, Yvan; Merle, Frank; Raphaël, Pierre
2015
Stability of the blow-up profile of nonlinear heat equations from the dynamical system point of view. Zbl 0971.35038
Fermanian Kammerer, C.; Merle, F.; Zaag, H.
2000
Positive solutions of elliptic equations involving supercritical growth. Zbl 0742.35025
Merle, F.; Peletier, L. A.
1991
Dynamics near the ground state for the energy critical nonlinear heat equation in large dimensions. Zbl 1401.35178
Collot, Charles; Merle, Frank; Raphaël, Pierre
2017
Blow-up results of virial type for Zakharov equations. Zbl 0858.35117
Merle, Frank
1996
Blow up of the critical norm for some radial $$L^2$$ super critical nonlinear Schrödinger equations. Zbl 1188.35182
Merle, Frank; Raphaël, Pierre
2008
Isolatedness of characteristic points at blowup for a 1-dimensional semilinear wave equation. Zbl 1270.35320
Merle, Frank; Zaag, Hatem
2012
Nonexistence of blow-up solution with minimal $$L^2$$-mass for the critical gKdV equation. Zbl 1033.35102
Martel, Yvan; Merle, Frank
2002
Inelastic interaction of nearly equal solitons for the quartic gKdV equation. Zbl 1230.35121
Martel, Yvan; Merle, Frank
2011
Solutions of the focusing nonradial critical wave equation with the compactness property. Zbl 1348.35141
Duyckaerts, Thomas; Kenig, Carlos; Merle, Frank
2016
Type II blow up for the energy supercritical NLS. Zbl 1347.35215
Merle, Frank; Raphaël, Pierre; Rodnianski, Igor
2015
Stability of two soliton collision for nonintegrable gKdV equations. Zbl 1179.35291
Martel, Yvan; Merle, Frank
2009
Optimal bounds on positive blow-up solutions for a semilinear wave equation. Zbl 0989.35090
Antonini, Christophe; Merle, Frank
2001
The instability of Bourgain-Wang solutions for the $$L^2$$ critical NLS. Zbl 1294.35145
Merle, Frank; Raphaël, Pierre; Szeftel, Jeremie
2013
On growth rate near the blowup surface for semilinear wave equations. Zbl 1160.35478
Merle, Frank; Zaag, Hatem
2005
Limit of the solution of a nonlinear Schrödinger equation at blow-up time. Zbl 0681.35078
Merle, F.
1989
Stable self-similar blow-up dynamics for slightly $$L^{2}$$ super-critical NLS equations. Zbl 1204.35153
Merle, Frank; Raphaël, Pierre; Szeftel, Jeremie
2010
Blow up dynamics for smooth equivariant solutions to the energy critical Schrödinger map. (Dynamique explosive de solutions régulières équivariantes de l’application de Schrödinger map.) Zbl 1213.35139
Merle, Frank; Raphaël, Pierre; Rodnianski, Igor
2011
Asymptotic behaviour of positive solutions of elliptic equations with critical and supercritical growth. I: The radial case. Zbl 0719.35004
Merle, F.; Peletier, L. A.
1990
Dynamics near explicit stationary solutions in similarity variables for solutions of a semilinear wave equation in higher dimensions. Zbl 1339.35062
Merle, Frank; Zaag, Hatem
2016
Radial solutions to energy supercritical wave equations in odd dimensions. Zbl 1298.35119
Kenig, Carlos E.; Merle, Frank
2011
Blow-up behavior outside the origin for a semilinear wave equation in the radial case. Zbl 1222.35126
Merle, Frank; Zaag, Hatem
2011
Construction of multi-solitons for the energy-critical wave equation in dimension 5. Zbl 1359.35166
Martel, Yvan; Merle, Frank
2016
Asymptotic behaviour of positive solutions of elliptic equations with critical and supercritical growth. II: The nonradial case. Zbl 0771.35008
Merle, F.; Peletier, L. A.
1992
Codimension one threshold manifold for the critical gKdV equation. Zbl 1336.35315
Martel, Yvan; Merle, Frank; Nakanishi, Kenji; Raphaël, Pierre
2016
Scattering below critical energy for the radial 4D Yang-Mills equation and for the 2D corotational wave map system. Zbl 1170.35064
Côte, Raphaël; Kenig, Carlos E.; Merle, Frank
2008
Self-focusing on bounded domains. Zbl 0980.35154
2001
On collapsing ring blow-up solutions to the mass supercritical nonlinear Schrödinger equation. Zbl 1292.35283
Merle, Frank; Raphaël, Pierre; Szeftel, Jeremie
2014
Lower bounds for the blowup rate of solutions of the Zakharov equation in dimension two. Zbl 0856.35014
Merle, Frank
1996
Reconnection of vortex with the boundary and finite time quenching. Zbl 0910.35020
Merle, Frank; Zaag, Hatem
1997
Refined asymptotics around solitons for gKdV equations. Zbl 1137.35062
Martel, Yvan; Merle, Frank
2008
Strongly anisotropic type II blow up at an isolated point. Zbl 1436.35253
Collot, Charles; Merle, Frank; Raphaël, Pierre
2020
Concentration-compactness and universal profiles for the non-radial energy critical wave equation. Zbl 1339.35186
Duyckaerts, Thomas; Kenig, Carlos; Merle, Frank
2016
Modulation theory for the blowup of vector-valued nonlinear heat equations. Zbl 0814.35043
Filippas, Stathis; Merle, Frank
1995
Profiles for bounded solutions of dispersive equations, with applications to energy-critical wave and Schrödinger equations. Zbl 1320.35066
Duyckaerts, Thomas; Kenig, Carlos E.; Merle, Frank
2015
Description of the inelastic collision of two solitary waves for the BBM equation. Zbl 1200.35267
Martel, Yvan; Merle, Frank; Mizumachi, Tetsu
2010
On one blow up point solutions to the critical nonlinear Schrödinger equation. Zbl 1117.35075
Merle, Frank; Raphael, Pierre
2005
Limit behavior of saturated approximations of nonlinear Schrödinger equation. Zbl 0756.35094
Merle, F.
1992
O. D. E. type behavior of blow-up solutions of nonlinear heat equations. Zbl 1009.35039
Merle, Frank; Zaag, Hatem
2002
On blow up for the energy super critical defocusing nonlinear Schrödinger equations. Zbl 1487.35353
Merle, Frank; Raphaël, Pierre; Rodnianski, Igor; Szeftel, Jeremie
2022
On the implosion of a compressible fluid. II: Singularity formation. Zbl 1497.35385
Merle, Frank; Rapha\'&rsquo;el, Pierre; Rodnianski, Igor; Szeftel, Jeremie
2022
On the implosion of a compressible fluid. I: Smooth self-similar inviscid profiles. Zbl 1497.35384
Merle, Frank; Rapha\'&rsquo;el, Pierre; Rodnianski, Igor; Szeftel, Jeremie
2022
Soliton resolution for critical co-rotational wave maps and radial cubic wave equation. Zbl 1491.35292
Duyckaerts, Thomas; Kenig, Carlos; Martel, Yvan; Merle, Frank
2022
Decay estimates for nonradiative solutions of the energy-critical focusing wave equation. Zbl 1472.35050
Duyckaerts, Thomas; Kenig, Carlos; Merle, Frank
2021
Strongly anisotropic type II blow up at an isolated point. Zbl 1436.35253
Collot, Charles; Merle, Frank; Raphaël, Pierre
2020
On strongly anisotropic type I blowup. Zbl 1432.35124
Merle, Frank; Raphaël, Pierre; Szeftel, Jeremie
2020
Exterior energy bounds for the critical wave equation close to the ground state. Zbl 1450.35157
Duyckaerts, Thomas; Kenig, Carlos; Merle, Frank
2020
Scattering profile for global solutions of the energy-critical wave equation. Zbl 1437.35497
Duyckaerts, Thomas; Kenig, Carlos E.; Merle, Frank
2019
Inelasticity of soliton collisions for the 5D energy critical wave equation. Zbl 1408.76111
Martel, Yvan; Merle, Frank
2018
Universality of blow up profile for small blow up solutions to the energy critical wave map equation. Zbl 1421.35038
Duyckaerts, Thomas; Jia, Hao; Kenig, Carlos; Merle, Frank
2018
Blowup solutions to the semilinear wave equation with a stylized pyramid as a blowup surface. Zbl 1402.35181
Merle, Frank; Zaag, Hatem
2018
Soliton resolution along a sequence of times for the focusing energy critical wave equation. Zbl 1391.35276
Duyckaerts, Thomas; Jia, Hao; Kenig, Carlos; Merle, Frank
2017
Dynamics near the ground state for the energy critical nonlinear heat equation in large dimensions. Zbl 1401.35178
Collot, Charles; Merle, Frank; Raphaël, Pierre
2017
Stability of ODE blow-up for the energy critical semilinear heat equation. (Stabilité de l’explosion type EDO pour l’équation de la chaleur énergie critique.) Zbl 1364.35156
Collot, Charles; Merle, Frank; Raphaël, Pierre
2017
Solutions of the focusing nonradial critical wave equation with the compactness property. Zbl 1348.35141
Duyckaerts, Thomas; Kenig, Carlos; Merle, Frank
2016
Dynamics near explicit stationary solutions in similarity variables for solutions of a semilinear wave equation in higher dimensions. Zbl 1339.35062
Merle, Frank; Zaag, Hatem
2016
Construction of multi-solitons for the energy-critical wave equation in dimension 5. Zbl 1359.35166
Martel, Yvan; Merle, Frank
2016
Codimension one threshold manifold for the critical gKdV equation. Zbl 1336.35315
Martel, Yvan; Merle, Frank; Nakanishi, Kenji; Raphaël, Pierre
2016
Concentration-compactness and universal profiles for the non-radial energy critical wave equation. Zbl 1339.35186
Duyckaerts, Thomas; Kenig, Carlos; Merle, Frank
2016
Global existence for solutions of the focusing wave equation with the compactness property. Zbl 1362.35190
Duyckaerts, Thomas; Kenig, Carlos; Merle, Frank
2016
On the stability of the notion of non-characteristic point and blow-up profile for semilinear wave equations. Zbl 1315.35134
Merle, Frank; Zaag, Hatem
2015
Blow up for the critical gKdV equation. III: Exotic regimes. Zbl 1331.35307
Martel, Yvan; Merle, Frank; Raphaël, Pierre
2015
Blow up for the critical gKdV equation. II: Minimal mass dynamics. Zbl 1326.35320
Martel, Yvan; Merle, Frank; Raphaël, Pierre
2015
Type II blow up for the energy supercritical NLS. Zbl 1347.35215
Merle, Frank; Raphaël, Pierre; Rodnianski, Igor
2015
Profiles for bounded solutions of dispersive equations, with applications to energy-critical wave and Schrödinger equations. Zbl 1320.35066
Duyckaerts, Thomas; Kenig, Carlos E.; Merle, Frank
2015
On the nonexistence of pure multi-solitons for the quartic gKdV equation. Zbl 1315.35191
Martel, Yvan; Merle, Frank
2015
Blow up for the critical generalized Korteweg-de Vries equation. I: Dynamics near the soliton. Zbl 1301.35137
Martel, Yvan; Merle, Frank; Raphaël, Pierre
2014
Scattering for radial, bounded solutions of focusing supercritical wave equations. Zbl 1310.35171
Duyckaerts, Thomas; Kenig, Carlos; Merle, Frank
2014
On collapsing ring blow-up solutions to the mass supercritical nonlinear Schrödinger equation. Zbl 1292.35283
Merle, Frank; Raphaël, Pierre; Szeftel, Jeremie
2014
Near soliton dynamics and singularity formation for $$L^2$$ critical problems. Zbl 1304.35650
Martel, Y.; Merle, F.; Raphaël, P.; Szeftel, J.
2014
Asymptotics for critical nonlinear dispersive equations. Zbl 1373.35049
Merle, Frank
2014
Classification of the radial solutions of the focusing, energy-critical wave equation. Zbl 1308.35143
Duyckaerts, Thomas; Kenig, Carlos; Merle, Frank
2013
Blowup dynamics for smooth data equivariant solutions to the critical Schrödinger map problem. Zbl 1326.35052
Merle, Frank; Raphaël, Pierre; Rodnianski, Igor
2013
The instability of Bourgain-Wang solutions for the $$L^2$$ critical NLS. Zbl 1294.35145
Merle, Frank; Raphaël, Pierre; Szeftel, Jeremie
2013
Blow up and near soliton dynamics for the $$L^2$$ critical gKdV equation. Zbl 1319.35224
Martel, Yvan; Merle, Frank; Raphaël, Pierre
2013
Profiles of bounded radial solutions of the focusing, energy-critical wave equation. Zbl 1258.35148
Duyckaerts, Thomas; Kenig, Carlos; Merle, Frank
2012
Universality of the blow-up profile for small type II blow-up solutions of the energy-critical wave equation: the nonradial case. Zbl 1282.35088
Duyckaerts, Thomas; Kenig, Carlos E.; Merle, Frank
2012
Existence and classification of characteristic points at blow-up for a semilinear wave equation in one space dimension. Zbl 1252.35204
Merle, Frank; Zaag, Hatem
2012
Isolatedness of characteristic points at blowup for a 1-dimensional semilinear wave equation. Zbl 1270.35320
Merle, Frank; Zaag, Hatem
2012
Isolatedness of characteristic points at blow-up for a semilinear wave equation in one space dimension. Zbl 1280.35019
Merle, Frank
2012
Two blow-up regimes for $$L^2$$. Zbl 1280.35140
Merle, Frank; Raphaël, Pierre; Szeftel, Jérémie
2012
Universality of blow-up profile for small radial type II blow-up solutions of the energy-critical wave equation. Zbl 1230.35067
Duyckaerts, Thomas; Kenig, Carlos; Merle, Frank
2011
Construction of multi-soliton solutions for the $$L^2$$-supercritical gKdV and NLS equations. Zbl 1273.35234
Côte, Raphaël; Martel, Yvan; Merle, Frank
2011
Nondispersive radial solutions to energy supercritical non-linear wave equations, with applications. Zbl 1241.35136
Kenig, Carlos E.; Merle, Frank
2011
Description of two soliton collision for the quartic gKdV equation. Zbl 1300.37045
Martel, Yvan; Merle, Frank
2011
Threshold and generic type I behaviors for a supercritical nonlinear heat equation. Zbl 1223.35088
Matano, Hiroshi; Merle, Frank
2011
Inelastic interaction of nearly equal solitons for the quartic gKdV equation. Zbl 1230.35121
Martel, Yvan; Merle, Frank
2011
Blow up dynamics for smooth equivariant solutions to the energy critical Schrödinger map. (Dynamique explosive de solutions régulières équivariantes de l’application de Schrödinger map.) Zbl 1213.35139
Merle, Frank; Raphaël, Pierre; Rodnianski, Igor
2011
Radial solutions to energy supercritical wave equations in odd dimensions. Zbl 1298.35119
Kenig, Carlos E.; Merle, Frank
2011
Blow-up behavior outside the origin for a semilinear wave equation in the radial case. Zbl 1222.35126
Merle, Frank; Zaag, Hatem
2011
Review of long time asymptotics and collision of solitons for the quartic generalized Korteweg-de Vries equation. Zbl 1219.35248
Martel, Yvan; Merle, Frank
2011
Maximizers for the Strichartz norm for small solutions of mass-critical NLS. Zbl 1247.35142
Duyckaerts, Thomas; Merle, Frank; Roudenko, Svetlana
2011
Scattering for $$\dot {H}^{1/2}$$ bounded solutions to the cubic, defocusing NLS in 3 dimensions. Zbl 1188.35180
Kenig, Carlos E.; Merle, Frank
2010
Stable self-similar blow-up dynamics for slightly $$L^{2}$$ super-critical NLS equations. Zbl 1204.35153
Merle, Frank; Raphaël, Pierre; Szeftel, Jeremie
2010
Description of the inelastic collision of two solitary waves for the BBM equation. Zbl 1200.35267
Martel, Yvan; Merle, Frank; Mizumachi, Tetsu
2010
Inelastic interaction of nearly equal solitons for the BBM equation. Zbl 1188.35165
Martel, Yvan; Merle, Frank
2010
Dynamic of threshold solutions for energy-critical NLS. Zbl 1232.35150
Duyckaerts, Thomas; Merle, Frank
2009
Classification of type I and type II behaviors for a supercritical nonlinear heat equation. Zbl 1178.35084
Matano, Hiroshi; Merle, Frank
2009
Stability of two soliton collision for nonintegrable gKdV equations. Zbl 1179.35291
Martel, Yvan; Merle, Frank
2009
Scattering norm estimate near the threshold for energy-critical focusing semilinear wave equation. Zbl 1179.35189
Duyckaerts, Thomas; Merle, Frank
2009
Global well-posedness, scattering and blow-up for the energy-critical focusing non-linear wave equation. Zbl 1183.35202
Kenig, Carlos E.; Merle, Frank
2008
Dynamics of threshold solutions for energy-critical wave equation. Zbl 1159.35043
Duyckaerts, Thomas; Merle, Frank
2008
Asymptotic stability of solitons of the gKdV equations with general nonlinearity. Zbl 1153.35068
Martel, Yvan; Merle, Frank
2008
Openness of the set of non-characteristic points and regularity of the blow-up curve for the 1 D semilinear wave equation. Zbl 1159.35046
Merle, Frank; Zaag, Hatem
2008
Blow up of the critical norm for some radial $$L^2$$ super critical nonlinear Schrödinger equations. Zbl 1188.35182
Merle, Frank; Raphaël, Pierre
2008
Scattering below critical energy for the radial 4D Yang-Mills equation and for the 2D corotational wave map system. Zbl 1170.35064
Côte, Raphaël; Kenig, Carlos E.; Merle, Frank
2008
Refined asymptotics around solitons for gKdV equations. Zbl 1137.35062
Martel, Yvan; Merle, Frank
2008
Note on coupled linear systems related to two soliton collision for the quartic gKdV equation. Zbl 1188.35164
Martel, Yvan; Merle, Frank
2008
Existence and universality of the blow-up profile for the semilinear wave equation in one space dimension. Zbl 1133.35070
Merle, Frank; Zaag, Hatem
2007
Global well-posedness, scattering and blow-up for the energy-critical, focusing, nonlinear Schrödinger equation in the radial case. Zbl 1115.35125
Kenig, Carlos E.; Merle, Frank
2006
On a sharp lower bound on the blow-up rate for the $$L^2$$ critical nonlinear Schrödinger equation. Zbl 1075.35077
Merle, Frank; Raphaël, Pierre
2006
Multi solitary waves for nonlinear Schrödinger equations. Zbl 1133.35093
Martel, Yvan; Merle, Frank
2006
Stability in $$H^1$$ of the sum of $$K$$ solitary waves for some nonlinear Schrödinger equations. Zbl 1099.35134
Martel, Yvan; Merle, Frank; Tsai, Tai-Peng
2006
Proof of a spectral property related to the singularity formation for the $$L^{2}$$ critical nonlinear Schrödinger equation. Zbl 1100.35097
Fibich, Gadi; Merle, Frank; Raphaël, Pierre
2006
Asymptotic stability and Liouville theorem for scalar viscous conservation laws in cylinders. Zbl 1105.35051
Kenig, Carlos E.; Merle, Frank
2006
The blow-up dynamic and upper bound on the blow-up rate for critical nonlinear Schrödinger equation. Zbl 1185.35263
Merle, Frank; Raphaël, Pierre
2005
Profiles and quantization of the blow up mass for critical nonlinear Schrödinger equation. Zbl 1062.35137
Merle, Frank; Raphaël, Pierre
2005
Asymptotic stability of solitons of the subcritical gKdV equations revisited. Zbl 1064.35171
Martel, Yvan; Merle, Frank
2005
Determination of the blow-up rate for a critical semilinear wave equation. Zbl 1136.35055
Merle, Frank; Zaag, Hatem
2005
On growth rate near the blowup surface for semilinear wave equations. Zbl 1160.35478
Merle, Frank; Zaag, Hatem
2005
On one blow up point solutions to the critical nonlinear Schrödinger equation. Zbl 1117.35075
Merle, Frank; Raphael, Pierre
2005
On universality of blow up profile for $$L^2$$ critical nonlinear Schrödinger equation. Zbl 1067.35110
Merle, Frank; Raphaël, Pierre
2004
On nonexistence of type II blowup for a supercritical nonlinear heat equation. Zbl 1112.35098
Matano, Hiroshi; Merle, Frank
2004
Review on blow up and asymptotic dynamics for critical and subcritical gKdV equations. Zbl 1071.35114
Martel, Yvan; Merle, Frank
2004
Sharp upper bound on the blow-up rate for the critical nonlinear Schrödinger equation. Zbl 1061.35135
Merle, Frank; Raphaël, Pierre
2003
Determination of the blow-up rate for the semilinear wave equation. Zbl 1052.35043
Merle, Frank; Zaag, Hatem
2003
$$L^2$$ stability of solitons for KdV equation. Zbl 1022.35061
Merle, F.; Vega, L.
2003
Qualitative results on the generalized critical KdV equation. Zbl 1044.35074
Martel, Yvan; Merle, Frank
2003
Stability and asymptotic stability for subcritical gKdV equations. Zbl 1017.35098
Martel, Yvan; Merle, Frank; Tsai, Tai-Peng
2002
Blow up in finite time and dynamics of blow up solutions for the $$L^2$$-critical generalized KdV equation. Zbl 0996.35064
Martel, Yvan; Merle, Frank
2002
Stability of blow-up profile and lower bounds for blow-up rate for the critical generalized KdV equation. Zbl 1005.35081
Martel, Yvan; Merle, Frank
2002
Nonexistence of blow-up solution with minimal $$L^2$$-mass for the critical gKdV equation. Zbl 1033.35102
Martel, Yvan; Merle, Frank
2002
O. D. E. type behavior of blow-up solutions of nonlinear heat equations. Zbl 1009.35039
Merle, Frank; Zaag, Hatem
2002
Asymptotic stability of solitons for subcritical generalized KdV equations. Zbl 0981.35073
Martel, Yvan; Merle, Frank
2001
Existence of blow-up solutions in the energy space for the critical generalized KdV equation. Zbl 0970.35128
Merle, Frank
2001
Instability of solitons for the critical generalized Korteweg-de Vries equation. Zbl 0985.35071
Martel, Y.; Merle, F.
2001
Optimal bounds on positive blow-up solutions for a semilinear wave equation. Zbl 0989.35090
Antonini, Christophe; Merle, Frank
2001
Self-focusing on bounded domains. Zbl 0980.35154
2001
Uniform blow-up estimates for nonlinear heat equations and applications. Zbl 1019.35044
Merle, Frank; Zaag, Hatem
2001
...and 38 more Documents
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### Cited by 1,493 Authors

 73 Merle, Frank 45 Martel, Yvan 45 Zaag, Hatem 44 Wei, Juncheng 40 Raphael, Pierre 34 Kenig, Carlos Eduardo 32 Bartolucci, Daniele 31 Lin, Chang-Shou 28 Muñoz, Claudio 25 Musso, Monica 24 Krieger, Joachim 24 Zhang, Jian 22 Saanouni, Tarek 21 Duyckaerts, Thomas 20 Roudenko, Svetlana 20 Zhu, Shihui 19 Miao, Changxing 19 Nakanishi, Kenji 19 Zhao, Lifeng 18 Côte, Raphaël 18 Del Pino, Manuel A. 18 Ding, Yanheng 18 Schlag, Wilhelm 17 Donninger, Roland 17 Mizoguchi, Noriko 17 Souplet, Philippe 17 Tarantello, Gabriella 17 Zheng, Jiqiang 16 Holmer, Justin 16 Yang, Wen 16 Zhou, Chunqin 15 Dinh, Van Duong 15 Dodson, Benjamin G. 15 Guo, Boling 15 Lee, Youngae 15 Martinazzi, Luca 15 Visan, Monica 14 Farah, Luiz Gustavo 14 Lawrie, Andrew G. W. 14 Malchiodi, Andrea 14 Tataru, Daniel 13 Cuccagna, Scipio 13 Ghoul, Tej-Eddine 13 Jevnikar, Aleks Yang Wen 13 Murphy, Jason 13 Suzuki, Takashi 13 Xu, Guixiang 13 Zhang, Xiaoyi 12 Ibrahim, Slim 12 Killip, Rowan 12 Kowalczyk, Michał 12 Nguyen, Van Tien 12 Wang, Guofang 12 Yang, Kai 11 Bahouri, Hajer 11 Jost, Jürgen 11 Maeda, Masaya 11 Masmoudi, Nader 11 Miyamoto, Yasuhito 10 Cazenave, Thierry 10 Jendrej, Jacek 10 Liu, Yue 10 Zhang, Lei 9 Carles, Rémi 9 Collot, Charles 9 Fibich, Gadi 9 Guzmán, Carlos M. 9 Hamza, Mohamed Ali 9 Li, Dong 9 Pastor, Ademir 9 Pistoia, Angela 9 Szeftel, Jérémie 9 Tzvetkov, Nikolay 8 Colliander, James E. 8 Deng, Shengbing 8 Fang, Daoyuan 8 Gan, Zaihui 8 Gao, Yanfang 8 Grossi, Massimo 8 Guo, Zihua 8 Klein, Christian 8 Lei, Yutian 8 Lenzmann, Enno 8 Li, Xiaoguang 8 Pausader, Benoît 8 Perelman, Galina 8 Struwe, Michael 8 Tao, Terence 8 Visciglia, Nicola 8 Wang, Zhong 8 Zhang, Jian 8 Zhao, Zehua 7 Akahori, Takafumi 7 Banica, Valeria 7 Cheng, Xing 7 Cho, Yonggeun 7 Choe, Kwangseok 7 D’Aprile, Teresa 7 Forcella, Luigi 7 Galaktionov, Victor Aleksandrovich ...and 1,393 more Authors
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### Cited in 249 Serials

 151 Journal of Differential Equations 99 Journal of Functional Analysis 84 Calculus of Variations and Partial Differential Equations 82 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 78 Journal of Mathematical Analysis and Applications 77 Communications in Mathematical Physics 65 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 62 Communications in Partial Differential Equations 54 Discrete and Continuous Dynamical Systems 51 Transactions of the American Mathematical Society 48 Journal of Mathematical Physics 41 Archive for Rational Mechanics and Analysis 36 Communications on Pure and Applied Analysis 33 Mathematische Annalen 29 Journal de Mathématiques Pures et Appliquées. Neuvième Série 27 Physica D 26 Communications in Contemporary Mathematics 25 Duke Mathematical Journal 24 Proceedings of the American Mathematical Society 24 SIAM Journal on Mathematical Analysis 24 Séminaire Laurent Schwartz. EDP et Applications 23 Advances in Mathematics 21 Acta Mathematica Sinica. English Series 20 Nonlinearity 20 Inventiones Mathematicae 19 NoDEA. Nonlinear Differential Equations and Applications 19 Journal of Evolution Equations 19 Annals of PDE 18 Journal of Hyperbolic Differential Equations 18 Analysis & PDE 17 Communications on Pure and Applied Mathematics 17 Comptes Rendus. Mathématique. Académie des Sciences, Paris 15 Applicable Analysis 14 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 14 Journal of the European Mathematical Society (JEMS) 13 ZAMP. Zeitschrift für angewandte Mathematik und Physik 12 Journal d’Analyse Mathématique 12 Journal of the American Mathematical Society 12 Journal of Dynamics and Differential Equations 12 Science China. Mathematics 11 Annali di Matematica Pura ed Applicata. Serie Quarta 11 Nonlinear Analysis. Real World Applications 10 Revista Matemática Iberoamericana 10 The Journal of Geometric Analysis 9 Applied Mathematics Letters 9 Nonlinear Analysis. Theory, Methods & Applications 8 Mathematical Methods in the Applied Sciences 8 Applied Mathematics and Computation 8 Mathematische Zeitschrift 8 Journal of Nonlinear Science 8 Discrete and Continuous Dynamical Systems. Series B 8 Advanced Nonlinear Studies 7 Memoirs of the American Mathematical Society 7 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 7 Geometric and Functional Analysis. GAFA 7 Bulletin des Sciences Mathématiques 7 Annales Henri Poincaré 7 Boundary Value Problems 6 Journal of Computational Physics 6 Bulletin of the American Mathematical Society. New Series 6 Annals of Mathematics. Second Series 6 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V 6 Discrete and Continuous Dynamical Systems. Series S 6 Advances in Nonlinear Analysis 5 Reviews in Mathematical Physics 5 Indiana University Mathematics Journal 5 Manuscripta Mathematica 5 Monatshefte für Mathematik 5 Chinese Annals of Mathematics. Series B 5 Asymptotic Analysis 5 Communications in Nonlinear Science and Numerical Simulation 5 Milan Journal of Mathematics 4 Computers & Mathematics with Applications 4 Annales de l’Institut Fourier 4 Bulletin de la Société Mathématique de France 4 Journal of Computational and Applied Mathematics 4 SIAM Journal on Numerical Analysis 4 SIAM Journal on Scientific Computing 4 Journal of Inequalities and Applications 4 Communications in Mathematics and Statistics 4 Journal of Elliptic and Parabolic Equations 4 SN Partial Differential Equations and Applications 3 Rocky Mountain Journal of Mathematics 3 Mathematics of Computation 3 Acta Mathematica 3 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 3 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 3 Illinois Journal of Mathematics 3 Journal of the Korean Mathematical Society 3 Journal für die Reine und Angewandte Mathematik 3 Pacific Journal of Mathematics 3 Proceedings of the Edinburgh Mathematical Society. Series II 3 Proceedings of the London Mathematical Society. Third Series 3 Acta Applicandae Mathematicae 3 Applied Numerical Mathematics 3 Annales de l’Institut Henri Poincaré. Physique Théorique 3 Potential Analysis 3 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 3 Mediterranean Journal of Mathematics 3 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis ...and 149 more Serials
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### Cited in 46 Fields

 1,911 Partial differential equations (35-XX) 145 Dynamical systems and ergodic theory (37-XX) 132 Quantum theory (81-XX) 128 Fluid mechanics (76-XX) 126 Global analysis, analysis on manifolds (58-XX) 86 Differential geometry (53-XX) 71 Numerical analysis (65-XX) 59 Operator theory (47-XX) 55 Statistical mechanics, structure of matter (82-XX) 49 Calculus of variations and optimal control; optimization (49-XX) 42 Functional analysis (46-XX) 38 Ordinary differential equations (34-XX) 38 Optics, electromagnetic theory (78-XX) 27 Harmonic analysis on Euclidean spaces (42-XX) 24 Biology and other natural sciences (92-XX) 21 Real functions (26-XX) 20 Mechanics of deformable solids (74-XX) 14 Functions of a complex variable (30-XX) 13 Probability theory and stochastic processes (60-XX) 12 Potential theory (31-XX) 12 Mechanics of particles and systems (70-XX) 12 Relativity and gravitational theory (83-XX) 10 Systems theory; control (93-XX) 9 Astronomy and astrophysics (85-XX) 8 Integral equations (45-XX) 5 Special functions (33-XX) 4 Difference and functional equations (39-XX) 4 Classical thermodynamics, heat transfer (80-XX) 3 Measure and integration (28-XX) 3 Several complex variables and analytic spaces (32-XX) 3 Statistics (62-XX) 2 History and biography (01-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 2 Nonassociative rings and algebras (17-XX) 2 Group theory and generalizations (20-XX) 2 Abstract harmonic analysis (43-XX) 2 Geophysics (86-XX) 1 General and overarching topics; collections (00-XX) 1 Algebraic geometry (14-XX) 1 Category theory; homological algebra (18-XX) 1 Topological groups, Lie groups (22-XX) 1 Approximations and expansions (41-XX) 1 Integral transforms, operational calculus (44-XX) 1 Manifolds and cell complexes (57-XX) 1 Computer science (68-XX) 1 Operations research, mathematical programming (90-XX)

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