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Author ID: merle.frank Recent zbMATH articles by "Merle, Frank"
Published as: Merle, Frank; Merle, F.; Merle, Franck
Homepage: https://www.ihes.fr/en/professeur/frank-merle-2/
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Serials

16 Communications in Mathematical Physics
10 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 Acta Mathematica
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 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 Advances in Mathematics
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

Publications by Year

Citations contained in zbMATH Open

142 Publications have been cited 5,804 times in 2,203 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
397
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
385
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
235
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
160
2005
Determination of blow-up solutions with minimal mass for nonlinear Schrödinger equations with critical power. Zbl 0808.35141
Merle, F.
130
1993
On universality of blow up profile for \(L^2\) critical nonlinear Schrödinger equation. Zbl 1067.35110
Merle, Frank; Raphaël, Pierre
120
2004
Construction of solutions with exactly k blow-up points for the Schrödinger equation with critical nonlinearity. Zbl 0707.35021
Merle, Frank
116
1990
Stability and asymptotic stability for subcritical gKdV equations. Zbl 1017.35098
Martel, Yvan; Merle, Frank; Tsai, Tai-Peng
108
2002
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
101
2006
Compactness at blow-up time for \(L^2\) solutions of the critical nonlinear Schrödinger equation in 2D. Zbl 0913.35126
Merle, F.; Vega, L.
96
1998
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
92
2011
Classification of the radial solutions of the focusing, energy-critical wave equation. Zbl 1308.35143
Duyckaerts, Thomas; Kenig, Carlos; Merle, Frank
89
2013
Sharp upper bound on the blow-up rate for the critical nonlinear Schrödinger equation. Zbl 1061.35135
Merle, Frank; Raphaël, Pierre
89
2003
Asymptotic stability of solitons for subcritical generalized KdV equations. Zbl 0981.35073
Martel, Yvan; Merle, Frank
89
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
88
1997
Profiles and quantization of the blow up mass for critical nonlinear Schrödinger equation. Zbl 1062.35137
Merle, Frank; Raphaël, Pierre
88
2005
L\({}^ 2\) concentration of blow-up solutions for the nonlinear Schrödinger equation with critical power nonlinearity. Zbl 0722.35047
Merle, Frank; Tsutsumi, Yoshio
87
1990
On nonexistence of type II blowup for a supercritical nonlinear heat equation. Zbl 1112.35098
Matano, Hiroshi; Merle, Frank
86
2004
Existence of blow-up solutions in the energy space for the critical generalized KdV equation. Zbl 0970.35128
Merle, Frank
78
2001
A Liouville theorem for the critical generalized Korteweg-de Vries equation. Zbl 0963.37058
Martel, Yvan; Merle, Frank
73
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
72
2002
Asymptotic stability of solitons of the subcritical gKdV equations revisited. Zbl 1064.35171
Martel, Yvan; Merle, Frank
69
2005
Instability of solitons for the critical generalized Korteweg-de Vries equation. Zbl 0985.35071
Martel, Y.; Merle, F.
68
2001
Dynamic of threshold solutions for energy-critical NLS. Zbl 1232.35150
Duyckaerts, Thomas; Merle, Frank
68
2009
Multi solitary waves for nonlinear Schrödinger equations. Zbl 1133.35093
Martel, Yvan; Merle, Frank
67
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
65
2006
Construction of multi-soliton solutions for the \(L^2\)-supercritical gKdV and NLS equations. Zbl 1273.35234
Côte, Raphaël; Martel, Yvan; Merle, Frank
64
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
64
2010
Profiles of bounded radial solutions of the focusing, energy-critical wave equation. Zbl 1258.35148
Duyckaerts, Thomas; Kenig, Carlos; Merle, Frank
63
2012
Dynamics of threshold solutions for energy-critical wave equation. Zbl 1159.35043
Duyckaerts, Thomas; Merle, Frank
62
2008
Classification of type I and type II behaviors for a supercritical nonlinear heat equation. Zbl 1178.35084
Matano, Hiroshi; Merle, Frank
60
2009
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
59
2002
Blowup dynamics for smooth data equivariant solutions to the critical Schrödinger map problem. Zbl 1326.35052
Merle, Frank; Raphaël, Pierre; Rodnianski, Igor
59
2013
Quantization effects for \(-\Delta u=u(1-| u|^ 2)\) in \(\mathbb{R}^ 2\). Zbl 0809.35019
Brézis, Haïm; Merle, Frank; Rivière, Tristan
58
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
58
2012
Existence of stationary states for nonlinear Dirac equations. Zbl 0696.35154
Merle, F.
58
1988
Solution of a nonlinear heat equation with arbitrarily given blow-up points. Zbl 0785.35012
Merle, Frank
55
1992
Blow up for the critical generalized Korteweg-de Vries equation. I: Dynamics near the soliton. Zbl 1301.35137
Martel, Yvan; Merle, Frank; Raphaël, Pierre
53
2014
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
53
1996
A Liouville theorem for vector-valued nonlinear heat equations and applications. Zbl 0939.35086
Merle, Frank; Zaag, Hatem
50
2000
Optimal estimates for blowup rate and behavior for nonlinear heat equations. Zbl 0899.35044
Merle, Frank; Zaag, Hatem
49
1998
Determination of the blow-up rate for the semilinear wave equation. Zbl 1052.35043
Merle, Frank; Zaag, Hatem
48
2003
Nondispersive radial solutions to energy supercritical non-linear wave equations, with applications. Zbl 1241.35136
Kenig, Carlos E.; Merle, Frank
47
2011
Existence of excited states for a nonlinear Dirac field. Zbl 0696.35158
Balabane, Mikhael; Cazenave, Thierry; Douady, Adrien; Merle, Frank
46
1988
Asymptotic stability of solitons of the gKdV equations with general nonlinearity. Zbl 1153.35068
Martel, Yvan; Merle, Frank
45
2008
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
45
1992
Determination of the blow-up rate for a critical semilinear wave equation. Zbl 1136.35055
Merle, Frank; Zaag, Hatem
45
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
44
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
44
2012
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
43
2017
Existence of self-similar blow-up solutions for Zakharov equation in dimension two. I. Zbl 0808.35137
Glangetas, L.; Merle, F.
43
1994
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
39
2008
Description of two soliton collision for the quartic gKdV equation. Zbl 1300.37045
Martel, Yvan; Merle, Frank
39
2011
Blow up for the critical gKdV equation. III: Exotic regimes. Zbl 1331.35307
Martel, Yvan; Merle, Frank; Raphaël, Pierre
38
2015
Blow up for the critical gKdV equation. II: Minimal mass dynamics. Zbl 1326.35320
Martel, Yvan; Merle, Frank; Raphaël, Pierre
37
2015
Scattering for radial, bounded solutions of focusing supercritical wave equations. Zbl 1310.35171
Duyckaerts, Thomas; Kenig, Carlos; Merle, Frank
37
2014
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
36
2015
Concentration properties of blow-up solutions and instability results for Zakharov equation in dimension two. II. Zbl 0808.35138
Glangetas, L.; Merle, F.
36
1994
Refined uniform estimates at blow-up and applications for nonlinear heat equations. Zbl 0926.35024
Merle, F.; Zaag, H.
34
1998
\(L^2\) stability of solitons for KdV equation. Zbl 1022.35061
Merle, F.; Vega, L.
33
2003
Dynamics near the ground state for the energy critical nonlinear heat equation in large dimensions. Zbl 1401.35178
Collot, Charles; Merle, Frank; Raphaël, Pierre
32
2017
Blow up of the critical norm for some radial \(L^2\) super critical nonlinear Schrödinger equations. Zbl 1188.35182
Merle, Frank; Raphaël, Pierre
32
2008
Threshold and generic type I behaviors for a supercritical nonlinear heat equation. Zbl 1223.35088
Matano, Hiroshi; Merle, Frank
32
2011
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.
31
2000
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
31
2006
Inelastic interaction of nearly equal solitons for the quartic gKdV equation. Zbl 1230.35121
Martel, Yvan; Merle, Frank
31
2011
Positive solutions of elliptic equations involving supercritical growth. Zbl 0742.35025
Merle, F.; Peletier, L. A.
30
1991
Blow-up results of virial type for Zakharov equations. Zbl 0858.35117
Merle, Frank
30
1996
Isolatedness of characteristic points at blowup for a 1-dimensional semilinear wave equation. Zbl 1270.35320
Merle, Frank; Zaag, Hatem
29
2012
The instability of Bourgain-Wang solutions for the \(L^2\) critical NLS. Zbl 1294.35145
Merle, Frank; Raphaël, Pierre; Szeftel, Jeremie
27
2013
Type II blow up for the energy supercritical NLS. Zbl 1347.35215
Merle, Frank; Raphaël, Pierre; Rodnianski, Igor
26
2015
Solutions of the focusing nonradial critical wave equation with the compactness property. Zbl 1348.35141
Duyckaerts, Thomas; Kenig, Carlos; Merle, Frank
25
2016
Nonexistence of blow-up solution with minimal \(L^2\)-mass for the critical gKdV equation. Zbl 1033.35102
Martel, Yvan; Merle, Frank
25
2002
Optimal bounds on positive blow-up solutions for a semilinear wave equation. Zbl 0989.35090
Antonini, Christophe; Merle, Frank
24
2001
On growth rate near the blowup surface for semilinear wave equations. Zbl 1160.35478
Merle, Frank; Zaag, Hatem
23
2005
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
23
2011
Stability of two soliton collision for nonintegrable gKdV equations. Zbl 1179.35291
Martel, Yvan; Merle, Frank
22
2009
Stable self-similar blow-up dynamics for slightly \(L^{2}\) super-critical NLS equations. Zbl 1204.35153
Merle, Frank; Raphaël, Pierre; Szeftel, Jeremie
22
2010
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
21
2008
Codimension one threshold manifold for the critical gKdV equation. Zbl 1336.35315
Martel, Yvan; Merle, Frank; Nakanishi, Kenji; Raphaël, Pierre
20
2016
Limit of the solution of a nonlinear Schrödinger equation at blow-up time. Zbl 0681.35078
Merle, F.
20
1989
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.
19
1990
Self-focusing on bounded domains. Zbl 0980.35154
Fibich, Gadi; Merle, Frank
19
2001
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
18
2016
Radial solutions to energy supercritical wave equations in odd dimensions. Zbl 1298.35119
Kenig, Carlos E.; Merle, Frank
18
2011
Construction of multi-solitons for the energy-critical wave equation in dimension 5. Zbl 1359.35166
Martel, Yvan; Merle, Frank
18
2016
Blow-up behavior outside the origin for a semilinear wave equation in the radial case. Zbl 1222.35126
Merle, Frank; Zaag, Hatem
18
2011
On collapsing ring blow-up solutions to the mass supercritical nonlinear Schrödinger equation. Zbl 1292.35283
Merle, Frank; Raphaël, Pierre; Szeftel, Jeremie
17
2014
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.
17
1992
Strongly anisotropic type II blow up at an isolated point. Zbl 1436.35253
Collot, Charles; Merle, Frank; Raphaël, Pierre
16
2020
Lower bounds for the blowup rate of solutions of the Zakharov equation in dimension two. Zbl 0856.35014
Merle, Frank
14
1996
On blow up for the energy super critical defocusing nonlinear Schrödinger equations. Zbl 1487.35353
Merle, Frank; Raphaël, Pierre; Rodnianski, Igor; Szeftel, Jeremie
14
2022
Reconnection of vortex with the boundary and finite time quenching. Zbl 0910.35020
Merle, Frank; Zaag, Hatem
14
1997
Concentration-compactness and universal profiles for the non-radial energy critical wave equation. Zbl 1339.35186
Duyckaerts, Thomas; Kenig, Carlos; Merle, Frank
13
2016
Refined asymptotics around solitons for gKdV equations. Zbl 1137.35062
Martel, Yvan; Merle, Frank
13
2008
On the implosion of a compressible fluid. II: Singularity formation. Zbl 1497.35385
Merle, Frank; Rapha\'’el, Pierre; Rodnianski, Igor; Szeftel, Jeremie
13
2022
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
12
2015
Modulation theory for the blowup of vector-valued nonlinear heat equations. Zbl 0814.35043
Filippas, Stathis; Merle, Frank
12
1995
Scattering profile for global solutions of the energy-critical wave equation. Zbl 1437.35497
Duyckaerts, Thomas; Kenig, Carlos E.; Merle, Frank
11
2019
Description of the inelastic collision of two solitary waves for the BBM equation. Zbl 1200.35267
Martel, Yvan; Merle, Frank; Mizumachi, Tetsu
11
2010
Soliton resolution for the radial critical wave equation in all odd space dimensions. Zbl 1520.35103
Duyckaerts, Thomas; Kenig, Carlos; Merle, Frank
5
2023
On blow up for the energy super critical defocusing nonlinear Schrödinger equations. Zbl 1487.35353
Merle, Frank; Raphaël, Pierre; Rodnianski, Igor; Szeftel, Jeremie
14
2022
On the implosion of a compressible fluid. II: Singularity formation. Zbl 1497.35385
Merle, Frank; Rapha\'’el, Pierre; Rodnianski, Igor; Szeftel, Jeremie
13
2022
On the implosion of a compressible fluid. I: Smooth self-similar inviscid profiles. Zbl 1497.35384
Merle, Frank; Rapha\'’el, Pierre; Rodnianski, Igor; Szeftel, Jeremie
11
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
7
2022
Behavior rigidity near non-isolated blow-up points for the semilinear heat equation. Zbl 1501.35092
Merle, Frank; Zaag, Hatem
2
2022
Decay estimates for nonradiative solutions of the energy-critical focusing wave equation. Zbl 1472.35050
Duyckaerts, Thomas; Kenig, Carlos; Merle, Frank
6
2021
Strongly anisotropic type II blow up at an isolated point. Zbl 1436.35253
Collot, Charles; Merle, Frank; Raphaël, Pierre
16
2020
On strongly anisotropic type I blowup. Zbl 1432.35124
Merle, Frank; Raphaël, Pierre; Szeftel, Jeremie
11
2020
Exterior energy bounds for the critical wave equation close to the ground state. Zbl 1450.35157
Duyckaerts, Thomas; Kenig, Carlos; Merle, Frank
7
2020
Scattering profile for global solutions of the energy-critical wave equation. Zbl 1437.35497
Duyckaerts, Thomas; Kenig, Carlos E.; Merle, Frank
11
2019
Inelasticity of soliton collisions for the 5D energy critical wave equation. Zbl 1408.76111
Martel, Yvan; Merle, Frank
6
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
6
2018
Blowup solutions to the semilinear wave equation with a stylized pyramid as a blowup surface. Zbl 1402.35181
Merle, Frank; Zaag, Hatem
2
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
43
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
32
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
8
2017
Solutions of the focusing nonradial critical wave equation with the compactness property. Zbl 1348.35141
Duyckaerts, Thomas; Kenig, Carlos; Merle, Frank
25
2016
Codimension one threshold manifold for the critical gKdV equation. Zbl 1336.35315
Martel, Yvan; Merle, Frank; Nakanishi, Kenji; Raphaël, Pierre
20
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
18
2016
Construction of multi-solitons for the energy-critical wave equation in dimension 5. Zbl 1359.35166
Martel, Yvan; Merle, Frank
18
2016
Concentration-compactness and universal profiles for the non-radial energy critical wave equation. Zbl 1339.35186
Duyckaerts, Thomas; Kenig, Carlos; Merle, Frank
13
2016
Global existence for solutions of the focusing wave equation with the compactness property. Zbl 1362.35190
Duyckaerts, Thomas; Kenig, Carlos; Merle, Frank
3
2016
Blow up for the critical gKdV equation. III: Exotic regimes. Zbl 1331.35307
Martel, Yvan; Merle, Frank; Raphaël, Pierre
38
2015
Blow up for the critical gKdV equation. II: Minimal mass dynamics. Zbl 1326.35320
Martel, Yvan; Merle, Frank; Raphaël, Pierre
37
2015
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
36
2015
Type II blow up for the energy supercritical NLS. Zbl 1347.35215
Merle, Frank; Raphaël, Pierre; Rodnianski, Igor
26
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
12
2015
On the nonexistence of pure multi-solitons for the quartic gKdV equation. Zbl 1315.35191
Martel, Yvan; Merle, Frank
6
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
53
2014
Scattering for radial, bounded solutions of focusing supercritical wave equations. Zbl 1310.35171
Duyckaerts, Thomas; Kenig, Carlos; Merle, Frank
37
2014
On collapsing ring blow-up solutions to the mass supercritical nonlinear Schrödinger equation. Zbl 1292.35283
Merle, Frank; Raphaël, Pierre; Szeftel, Jeremie
17
2014
Near soliton dynamics and singularity formation for \( L^2\) critical problems. Zbl 1304.35650
Martel, Y.; Merle, F.; Raphaël, P.; Szeftel, J.
6
2014
Asymptotics for critical nonlinear dispersive equations. Zbl 1373.35049
Merle, Frank
1
2014
Classification of the radial solutions of the focusing, energy-critical wave equation. Zbl 1308.35143
Duyckaerts, Thomas; Kenig, Carlos; Merle, Frank
89
2013
Blowup dynamics for smooth data equivariant solutions to the critical Schrödinger map problem. Zbl 1326.35052
Merle, Frank; Raphaël, Pierre; Rodnianski, Igor
59
2013
The instability of Bourgain-Wang solutions for the \(L^2\) critical NLS. Zbl 1294.35145
Merle, Frank; Raphaël, Pierre; Szeftel, Jeremie
27
2013
Blow up and near soliton dynamics for the \(L^2\) critical gKdV equation. Zbl 1319.35224
Martel, Yvan; Merle, Frank; Raphaël, Pierre
6
2013
Profiles of bounded radial solutions of the focusing, energy-critical wave equation. Zbl 1258.35148
Duyckaerts, Thomas; Kenig, Carlos; Merle, Frank
63
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
58
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
44
2012
Isolatedness of characteristic points at blowup for a 1-dimensional semilinear wave equation. Zbl 1270.35320
Merle, Frank; Zaag, Hatem
29
2012
Isolatedness of characteristic points at blow-up for a semilinear wave equation in one space dimension. Zbl 1280.35019
Merle, Frank
2
2012
Two blow-up regimes for \(L^2\). Zbl 1280.35140
Merle, Frank; Raphaël, Pierre; Szeftel, Jérémie
1
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
92
2011
Construction of multi-soliton solutions for the \(L^2\)-supercritical gKdV and NLS equations. Zbl 1273.35234
Côte, Raphaël; Martel, Yvan; Merle, Frank
64
2011
Nondispersive radial solutions to energy supercritical non-linear wave equations, with applications. Zbl 1241.35136
Kenig, Carlos E.; Merle, Frank
47
2011
Description of two soliton collision for the quartic gKdV equation. Zbl 1300.37045
Martel, Yvan; Merle, Frank
39
2011
Threshold and generic type I behaviors for a supercritical nonlinear heat equation. Zbl 1223.35088
Matano, Hiroshi; Merle, Frank
32
2011
Inelastic interaction of nearly equal solitons for the quartic gKdV equation. Zbl 1230.35121
Martel, Yvan; Merle, Frank
31
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
23
2011
Radial solutions to energy supercritical wave equations in odd dimensions. Zbl 1298.35119
Kenig, Carlos E.; Merle, Frank
18
2011
Blow-up behavior outside the origin for a semilinear wave equation in the radial case. Zbl 1222.35126
Merle, Frank; Zaag, Hatem
18
2011
Maximizers for the Strichartz norm for small solutions of mass-critical NLS. Zbl 1247.35142
Duyckaerts, Thomas; Merle, Frank; Roudenko, Svetlana
6
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
6
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
64
2010
Stable self-similar blow-up dynamics for slightly \(L^{2}\) super-critical NLS equations. Zbl 1204.35153
Merle, Frank; Raphaël, Pierre; Szeftel, Jeremie
22
2010
Description of the inelastic collision of two solitary waves for the BBM equation. Zbl 1200.35267
Martel, Yvan; Merle, Frank; Mizumachi, Tetsu
11
2010
Inelastic interaction of nearly equal solitons for the BBM equation. Zbl 1188.35165
Martel, Yvan; Merle, Frank
6
2010
Dynamic of threshold solutions for energy-critical NLS. Zbl 1232.35150
Duyckaerts, Thomas; Merle, Frank
68
2009
Classification of type I and type II behaviors for a supercritical nonlinear heat equation. Zbl 1178.35084
Matano, Hiroshi; Merle, Frank
60
2009
Stability of two soliton collision for nonintegrable gKdV equations. Zbl 1179.35291
Martel, Yvan; Merle, Frank
22
2009
Scattering norm estimate near the threshold for energy-critical focusing semilinear wave equation. Zbl 1179.35189
Duyckaerts, Thomas; Merle, Frank
1
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
235
2008
Dynamics of threshold solutions for energy-critical wave equation. Zbl 1159.35043
Duyckaerts, Thomas; Merle, Frank
62
2008
Asymptotic stability of solitons of the gKdV equations with general nonlinearity. Zbl 1153.35068
Martel, Yvan; Merle, Frank
45
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
39
2008
Blow up of the critical norm for some radial \(L^2\) super critical nonlinear Schrödinger equations. Zbl 1188.35182
Merle, Frank; Raphaël, Pierre
32
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
21
2008
Refined asymptotics around solitons for gKdV equations. Zbl 1137.35062
Martel, Yvan; Merle, Frank
13
2008
Note on coupled linear systems related to two soliton collision for the quartic gKdV equation. Zbl 1188.35164
Martel, Yvan; Merle, Frank
4
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
44
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
385
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
101
2006
Multi solitary waves for nonlinear Schrödinger equations. Zbl 1133.35093
Martel, Yvan; Merle, Frank
67
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
65
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
31
2006
Asymptotic stability and Liouville theorem for scalar viscous conservation laws in cylinders. Zbl 1105.35051
Kenig, Carlos E.; Merle, Frank
7
2006
A note on a symmetry result for traveling waves in cylinders. Zbl 1085.35070
Kenig, C. E.; Merle, F.
1
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
160
2005
Profiles and quantization of the blow up mass for critical nonlinear Schrödinger equation. Zbl 1062.35137
Merle, Frank; Raphaël, Pierre
88
2005
Asymptotic stability of solitons of the subcritical gKdV equations revisited. Zbl 1064.35171
Martel, Yvan; Merle, Frank
69
2005
Determination of the blow-up rate for a critical semilinear wave equation. Zbl 1136.35055
Merle, Frank; Zaag, Hatem
45
2005
On growth rate near the blowup surface for semilinear wave equations. Zbl 1160.35478
Merle, Frank; Zaag, Hatem
23
2005
On one blow up point solutions to the critical nonlinear Schrödinger equation. Zbl 1117.35075
Merle, Frank; Raphael, Pierre
10
2005
On universality of blow up profile for \(L^2\) critical nonlinear Schrödinger equation. Zbl 1067.35110
Merle, Frank; Raphaël, Pierre
120
2004
On nonexistence of type II blowup for a supercritical nonlinear heat equation. Zbl 1112.35098
Matano, Hiroshi; Merle, Frank
86
2004
Review on blow up and asymptotic dynamics for critical and subcritical gKdV equations. Zbl 1071.35114
Martel, Yvan; Merle, Frank
2
2004
Sharp upper bound on the blow-up rate for the critical nonlinear Schrödinger equation. Zbl 1061.35135
Merle, Frank; Raphaël, Pierre
89
2003
Determination of the blow-up rate for the semilinear wave equation. Zbl 1052.35043
Merle, Frank; Zaag, Hatem
48
2003
\(L^2\) stability of solitons for KdV equation. Zbl 1022.35061
Merle, F.; Vega, L.
33
2003
Qualitative results on the generalized critical KdV equation. Zbl 1044.35074
Martel, Yvan; Merle, Frank
1
2003
Stability and asymptotic stability for subcritical gKdV equations. Zbl 1017.35098
Martel, Yvan; Merle, Frank; Tsai, Tai-Peng
108
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
72
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
59
2002
Nonexistence of blow-up solution with minimal \(L^2\)-mass for the critical gKdV equation. Zbl 1033.35102
Martel, Yvan; Merle, Frank
25
2002
O. D. E. type behavior of blow-up solutions of nonlinear heat equations. Zbl 1009.35039
Merle, Frank; Zaag, Hatem
9
2002
A Liouville theorem for the viscous Burgers’s equation. Zbl 1028.35130
Kenig, Carlos E.; Merle, Frank
1
2002
Asymptotic stability of solitons for subcritical generalized KdV equations. Zbl 0981.35073
Martel, Yvan; Merle, Frank
89
2001
Existence of blow-up solutions in the energy space for the critical generalized KdV equation. Zbl 0970.35128
Merle, Frank
78
2001
...and 42 more Documents
all top 5

Cited by 1,637 Authors

74 Merle, Frank
49 Zaag, Hatem
46 Martel, Yvan
46 Wei, Juncheng
42 Raphael, Pierre
38 Kenig, Carlos Eduardo
32 Bartolucci, Daniele
31 Lin, Chang-Shou
30 Muñoz, Claudio
28 Saanouni, Tarek
26 Zhang, Jian
25 Krieger, Joachim
25 Musso, Monica
22 Duyckaerts, Thomas
22 Miao, Changxing
21 Côte, Raphaël
20 Ding, Yanheng
20 Nakanishi, Kenji
20 Roudenko, Svetlana
20 Zhu, Shihui
19 Donninger, Roland
19 Lawrie, Andrew G. W.
19 Tarantello, Gabriella
19 Zhao, Lifeng
18 Del Pino, Manuel A.
18 Dinh, Van Duong
18 Mizoguchi, Noriko
18 Schlag, Wilhelm
18 Souplet, Philippe
18 Zheng, Jiqiang
17 Guo, Boling
17 Yang, Wen
16 Dodson, Benjamin G.
16 Holmer, Justin
16 Martinazzi, Luca
16 Murphy, Jason
16 Visan, Monica
16 Zhou, Chunqin
15 Farah, Luiz Gustavo
15 Jendrej, Jacek
15 Lee, Youngae
15 Tataru, Daniel
14 Ghoul, Tej-Eddine
14 Jevnikar, Aleks Yang Wen
14 Malchiodi, Andrea
14 Suzuki, Takashi
14 Xu, Guixiang
14 Zhang, Xiaoyi
13 Cuccagna, Scipio
13 Kowalczyk, Michał
13 Nguyen, Van Tien
13 Yang, Kai
12 Ibrahim, Slim
12 Killip, Rowan
12 Maeda, Masaya
12 Masmoudi, Nader
12 Wang, Guofang
11 Bahouri, Hajer
11 Collot, Charles
11 Jost, Jürgen
11 Miyamoto, Yasuhito
11 Tzvetkov, Nikolay
10 Cazenave, Thierry
10 Fibich, Gadi
10 Guo, Zihua
10 Guzmán, Carlos M.
10 Klein, Christian
10 Liu, Yue
10 Pistoia, Angela
10 Zhang, Lei
10 Zhao, Zehua
9 Carles, Rémi
9 Deng, Shengbing
9 Hamza, Mohamed Ali
9 Lei, Yutian
9 Lenzmann, Enno
9 Li, Dong
9 Ogawa, Takayoshi
9 Pastor, Ademir
9 Szeftel, Jérémie
9 Visciglia, Nicola
9 Wang, Zhong
8 Akahori, Takafumi
8 Banica, Valeria
8 Cheng, Xing
8 Cho, Yonggeun
8 Colliander, James E.
8 Duong, Giao Ky
8 Fang, Daoyuan
8 Gan, Zaihui
8 Gao, Yanfang
8 Grossi, Massimo
8 Hyder, Ali
8 Ikeda, Masahiro
8 Li, Xiaoguang
8 Li, Ze
8 Mizumachi, Tetsu
8 Nouaili, Nejla
8 Oh, Sung-Jin
8 Pausader, Benoît
...and 1,537 more Authors
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Cited in 260 Serials

163 Journal of Differential Equations
106 Journal of Functional Analysis
91 Calculus of Variations and Partial Differential Equations
88 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods
87 Communications in Mathematical Physics
84 Journal of Mathematical Analysis and Applications
68 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire
64 Communications in Partial Differential Equations
56 Discrete and Continuous Dynamical Systems
54 Transactions of the American Mathematical Society
53 Journal of Mathematical Physics
41 Archive for Rational Mechanics and Analysis
39 Communications on Pure and Applied Analysis
34 Mathematische Annalen
31 Physica D
31 Journal de Mathématiques Pures et Appliquées. Neuvième Série
31 SIAM Journal on Mathematical Analysis
29 Advances in Mathematics
26 Nonlinearity
26 Duke Mathematical Journal
26 Proceedings of the American Mathematical Society
26 Communications in Contemporary Mathematics
24 Séminaire Laurent Schwartz. EDP et Applications
23 Communications on Pure and Applied Mathematics
21 Acta Mathematica Sinica. English Series
21 Journal of Evolution Equations
21 Annals of PDE
20 Inventiones Mathematicae
19 NoDEA. Nonlinear Differential Equations and Applications
19 Analysis & PDE
18 Journal of Hyperbolic Differential Equations
17 Comptes Rendus. Mathématique. Académie des Sciences, Paris
16 Applicable Analysis
16 Journal of the European Mathematical Society (JEMS)
15 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics
14 ZAMP. Zeitschrift für angewandte Mathematik und Physik
13 Journal d’Analyse Mathématique
13 Revista Matemática Iberoamericana
13 Journal of Dynamics and Differential Equations
13 Science China. Mathematics
12 Journal of the American Mathematical Society
11 Mathematical Methods in the Applied Sciences
11 Annali di Matematica Pura ed Applicata. Serie Quarta
11 The Journal of Geometric Analysis
11 Nonlinear Analysis. Real World Applications
10 Applied Mathematics and Computation
9 Mathematische Zeitschrift
9 Memoirs of the American Mathematical Society
9 Applied Mathematics Letters
9 Annales Henri Poincaré
9 Advanced Nonlinear Studies
9 Nonlinear Analysis. Theory, Methods & Applications
8 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences
8 Geometric and Functional Analysis. GAFA
8 Journal of Nonlinear Science
8 Discrete and Continuous Dynamical Systems. Series B
8 Boundary Value Problems
8 Discrete and Continuous Dynamical Systems. Series S
7 Bulletin des Sciences Mathématiques
7 Advances in Nonlinear Analysis
6 Journal of Computational Physics
6 Indiana University Mathematics Journal
6 Monatshefte für Mathematik
6 Asymptotic Analysis
6 Bulletin of the American Mathematical Society. New Series
6 Annals of Mathematics. Second Series
6 Communications in Nonlinear Science and Numerical Simulation
6 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V
5 Reviews in Mathematical Physics
5 Manuscripta Mathematica
5 SIAM Journal on Numerical Analysis
5 Chinese Annals of Mathematics. Series B
5 Journal of Inequalities and Applications
5 Milan Journal of Mathematics
5 Journal of Fixed Point Theory and Applications
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 Quarterly of Applied Mathematics
4 Applied Numerical Mathematics
4 Journal of Scientific Computing
4 Potential Analysis
4 SIAM Journal on Scientific Computing
4 Vietnam Journal of Mathematics
4 Communications in Mathematics and Statistics
4 Journal of Elliptic and Parabolic Equations
4 Pure and Applied Analysis
4 SN Partial Differential Equations and Applications
3 Letters in Mathematical Physics
3 Rocky Mountain Journal of Mathematics
3 Mathematics of Computation
3 Acta Mathematica
3 American Journal of Mathematics
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 Mathematische Nachrichten
...and 160 more Serials
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Cited in 46 Fields

2,091 Partial differential equations (35-XX)
171 Dynamical systems and ergodic theory (37-XX)
149 Fluid mechanics (76-XX)
138 Quantum theory (81-XX)
134 Global analysis, analysis on manifolds (58-XX)
94 Differential geometry (53-XX)
82 Numerical analysis (65-XX)
63 Statistical mechanics, structure of matter (82-XX)
60 Operator theory (47-XX)
56 Calculus of variations and optimal control; optimization (49-XX)
47 Optics, electromagnetic theory (78-XX)
43 Functional analysis (46-XX)
36 Ordinary differential equations (34-XX)
34 Harmonic analysis on Euclidean spaces (42-XX)
27 Real functions (26-XX)
26 Biology and other natural sciences (92-XX)
21 Probability theory and stochastic processes (60-XX)
20 Mechanics of deformable solids (74-XX)
17 Functions of a complex variable (30-XX)
14 Relativity and gravitational theory (83-XX)
12 Potential theory (31-XX)
12 Mechanics of particles and systems (70-XX)
12 Systems theory; control (93-XX)
9 Astronomy and astrophysics (85-XX)
8 Integral equations (45-XX)
6 Classical thermodynamics, heat transfer (80-XX)
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