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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
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

Publications by Year

Citations contained in zbMATH Open

138 Publications have been cited 5,235 times in 1,990 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
378
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
359
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
224
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
142
2005
Determination of blow-up solutions with minimal mass for nonlinear Schrödinger equations with critical power. Zbl 0808.35141
Merle, F.
115
1993
On universality of blow up profile for \(L^2\) critical nonlinear Schrödinger equation. Zbl 1067.35110
Merle, Frank; Raphaël, Pierre
110
2004
Construction of solutions with exactly k blow-up points for the Schrödinger equation with critical nonlinearity. Zbl 0707.35021
Merle, Frank
103
1990
Stability and asymptotic stability for subcritical gKdV equations. Zbl 1017.35098
Martel, Yvan; Merle, Frank; Tsai, Tai-Peng
94
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.
90
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
89
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
86
2011
L\({}^ 2\) concentration of blow-up solutions for the nonlinear Schrödinger equation with critical power nonlinearity. Zbl 0722.35047
Merle, Frank; Tsutsumi, Yoshio
84
1990
On nonexistence of type II blowup for a supercritical nonlinear heat equation. Zbl 1112.35098
Matano, Hiroshi; Merle, Frank
84
2004
Sharp upper bound on the blow-up rate for the critical nonlinear Schrödinger equation. Zbl 1061.35135
Merle, Frank; Raphaël, Pierre
82
2003
Classification of the radial solutions of the focusing, energy-critical wave equation. Zbl 1308.35143
Duyckaerts, Thomas; Kenig, Carlos; Merle, Frank
81
2013
Profiles and quantization of the blow up mass for critical nonlinear Schrödinger equation. Zbl 1062.35137
Merle, Frank; Raphaël, Pierre
80
2005
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
78
1997
Asymptotic stability of solitons for subcritical generalized KdV equations. Zbl 0981.35073
Martel, Yvan; Merle, Frank
76
2001
Existence of blow-up solutions in the energy space for the critical generalized KdV equation. Zbl 0970.35128
Merle, Frank
69
2001
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
68
2002
A Liouville theorem for the critical generalized Korteweg-de Vries equation. Zbl 0963.37058
Martel, Yvan; Merle, Frank
67
2000
Instability of solitons for the critical generalized Korteweg-de Vries equation. Zbl 0985.35071
Martel, Y.; Merle, F.
64
2001
Dynamic of threshold solutions for energy-critical NLS. Zbl 1232.35150
Duyckaerts, Thomas; Merle, Frank
62
2009
Asymptotic stability of solitons of the subcritical gKdV equations revisited. Zbl 1064.35171
Martel, Yvan; Merle, Frank
60
2005
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
59
2006
Multi solitary waves for nonlinear Schrödinger equations. Zbl 1133.35093
Martel, Yvan; Merle, Frank
59
2006
Profiles of bounded radial solutions of the focusing, energy-critical wave equation. Zbl 1258.35148
Duyckaerts, Thomas; Kenig, Carlos; Merle, Frank
57
2012
Classification of type I and type II behaviors for a supercritical nonlinear heat equation. Zbl 1178.35084
Matano, Hiroshi; Merle, Frank
57
2009
Scattering for \(\dot {H}^{1/2}\) bounded solutions to the cubic, defocusing NLS in 3 dimensions. Zbl 1188.35180
Kenig, Carlos E.; Merle, Frank
56
2010
Dynamics of threshold solutions for energy-critical wave equation. Zbl 1159.35043
Duyckaerts, Thomas; Merle, Frank
55
2008
Existence of stationary states for nonlinear Dirac equations. Zbl 0696.35154
Merle, F.
55
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
55
2002
Quantization effects for \(-\Delta u=u(1-| u|^ 2)\) in \(\mathbb{R}^ 2\). Zbl 0809.35019
Brézis, Haïm; Merle, Frank; Rivière, Tristan
54
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
54
2012
Construction of multi-soliton solutions for the \(L^2\)-supercritical gKdV and NLS equations. Zbl 1273.35234
Côte, Raphaël; Martel, Yvan; Merle, Frank
54
2011
Solution of a nonlinear heat equation with arbitrarily given blow-up points. Zbl 0785.35012
Merle, Frank
53
1992
Blowup dynamics for smooth data equivariant solutions to the critical Schrödinger map problem. Zbl 1326.35052
Merle, Frank; Raphaël, Pierre; Rodnianski, Igor
50
2013
A Liouville theorem for vector-valued nonlinear heat equations and applications. Zbl 0939.35086
Merle, Frank; Zaag, Hatem
49
2000
Determination of the blow-up rate for the semilinear wave equation. Zbl 1052.35043
Merle, Frank; Zaag, Hatem
46
2003
Nondispersive radial solutions to energy supercritical non-linear wave equations, with applications. Zbl 1241.35136
Kenig, Carlos E.; Merle, Frank
45
2011
Existence of excited states for a nonlinear Dirac field. Zbl 0696.35158
Balabane, Mikhael; Cazenave, Thierry; Douady, Adrien; Merle, Frank
44
1988
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
43
1992
Determination of the blow-up rate for a critical semilinear wave equation. Zbl 1136.35055
Merle, Frank; Zaag, Hatem
43
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
42
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
41
2012
Existence of self-similar blow-up solutions for Zakharov equation in dimension two. I. Zbl 0808.35137
Glangetas, L.; Merle, F.
41
1994
Asymptotic stability of solitons of the gKdV equations with general nonlinearity. Zbl 1153.35068
Martel, Yvan; Merle, Frank
41
2008
Optimal estimates for blowup rate and behavior for nonlinear heat equations. Zbl 0899.35044
Merle, Frank; Zaag, Hatem
40
1998
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
40
1996
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
38
2008
Blow up for the critical generalized Korteweg-de Vries equation. I: Dynamics near the soliton. Zbl 1301.35137
Martel, Yvan; Merle, Frank; Raphaël, Pierre
38
2014
Scattering for radial, bounded solutions of focusing supercritical wave equations. Zbl 1310.35171
Duyckaerts, Thomas; Kenig, Carlos; Merle, Frank
35
2014
Concentration properties of blow-up solutions and instability results for Zakharov equation in dimension two. II. Zbl 0808.35138
Glangetas, L.; Merle, F.
35
1994
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
34
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
33
2015
Refined uniform estimates at blow-up and applications for nonlinear heat equations. Zbl 0926.35024
Merle, F.; Zaag, H.
32
1998
Description of two soliton collision for the quartic gKdV equation. Zbl 1300.37045
Martel, Yvan; Merle, Frank
32
2011
Blow up for the critical gKdV equation. III: Exotic regimes. Zbl 1331.35307
Martel, Yvan; Merle, Frank; Raphaël, Pierre
31
2015
Threshold and generic type I behaviors for a supercritical nonlinear heat equation. Zbl 1223.35088
Matano, Hiroshi; Merle, Frank
30
2011
\(L^2\) stability of solitons for KdV equation. Zbl 1022.35061
Merle, F.; Vega, L.
30
2003
Blow up for the critical gKdV equation. II: Minimal mass dynamics. Zbl 1326.35320
Martel, Yvan; Merle, Frank; Raphaël, Pierre
29
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.
29
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
29
2006
Positive solutions of elliptic equations involving supercritical growth. Zbl 0742.35025
Merle, F.; Peletier, L. A.
28
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
28
2017
Blow-up results of virial type for Zakharov equations. Zbl 0858.35117
Merle, Frank
27
1996
Isolatedness of characteristic points at blowup for a 1-dimensional semilinear wave equation. Zbl 1270.35320
Merle, Frank; Zaag, Hatem
26
2012
Blow up of the critical norm for some radial \(L^2\) super critical nonlinear Schrödinger equations. Zbl 1188.35182
Merle, Frank; Raphaël, Pierre
26
2008
Nonexistence of blow-up solution with minimal \(L^2\)-mass for the critical gKdV equation. Zbl 1033.35102
Martel, Yvan; Merle, Frank
25
2002
Inelastic interaction of nearly equal solitons for the quartic gKdV equation. Zbl 1230.35121
Martel, Yvan; Merle, Frank
24
2011
Solutions of the focusing nonradial critical wave equation with the compactness property. Zbl 1348.35141
Duyckaerts, Thomas; Kenig, Carlos; Merle, Frank
23
2016
Type II blow up for the energy supercritical NLS. Zbl 1347.35215
Merle, Frank; Raphaël, Pierre; Rodnianski, Igor
22
2015
Stability of two soliton collision for nonintegrable gKdV equations. Zbl 1179.35291
Martel, Yvan; Merle, Frank
22
2009
Optimal bounds on positive blow-up solutions for a semilinear wave equation. Zbl 0989.35090
Antonini, Christophe; Merle, Frank
22
2001
On growth rate near the blowup surface for semilinear wave equations. Zbl 1160.35478
Merle, Frank; Zaag, Hatem
21
2005
The instability of Bourgain-Wang solutions for the \(L^2\) critical NLS. Zbl 1294.35145
Merle, Frank; Raphaël, Pierre; Szeftel, Jeremie
21
2013
Limit of the solution of a nonlinear Schrödinger equation at blow-up time. Zbl 0681.35078
Merle, F.
20
1989
Stable self-similar blow-up dynamics for slightly \(L^{2}\) super-critical NLS equations. Zbl 1204.35153
Merle, Frank; Raphaël, Pierre; Szeftel, Jeremie
20
2010
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
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
19
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
Radial solutions to energy supercritical wave equations in odd dimensions. Zbl 1298.35119
Kenig, Carlos E.; Merle, Frank
18
2011
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
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
Codimension one threshold manifold for the critical gKdV equation. Zbl 1336.35315
Martel, Yvan; Merle, Frank; Nakanishi, Kenji; Raphaël, Pierre
17
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
17
2008
Construction of multi-solitons for the energy-critical wave equation in dimension 5. Zbl 1359.35166
Martel, Yvan; Merle, Frank
17
2016
Self-focusing on bounded domains. Zbl 0980.35154
Fibich, Gadi; Merle, Frank
16
2001
On collapsing ring blow-up solutions to the mass supercritical nonlinear Schrödinger equation. Zbl 1292.35283
Merle, Frank; Raphaël, Pierre; Szeftel, Jeremie
14
2014
Lower bounds for the blowup rate of solutions of the Zakharov equation in dimension two. Zbl 0856.35014
Merle, Frank
13
1996
Reconnection of vortex with the boundary and finite time quenching. Zbl 0910.35020
Merle, Frank; Zaag, Hatem
13
1997
Refined asymptotics around solitons for gKdV equations. Zbl 1137.35062
Martel, Yvan; Merle, Frank
13
2008
Concentration-compactness and universal profiles for the non-radial energy critical wave equation. Zbl 1339.35186
Duyckaerts, Thomas; Kenig, Carlos; Merle, Frank
12
2016
Strongly anisotropic type II blow up at an isolated point. Zbl 1436.35253
Collot, Charles; Merle, Frank; Raphaël, Pierre
12
2020
Modulation theory for the blowup of vector-valued nonlinear heat equations. Zbl 0814.35043
Filippas, Stathis; Merle, Frank
12
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
11
2015
Description of the inelastic collision of two solitary waves for the BBM equation. Zbl 1200.35267
Martel, Yvan; Merle, Frank; Mizumachi, Tetsu
10
2010
Limit behavior of saturated approximations of nonlinear Schrödinger equation. Zbl 0756.35094
Merle, F.
9
1992
On one blow up point solutions to the critical nonlinear Schrödinger equation. Zbl 1117.35075
Merle, Frank; Raphael, Pierre
9
2005
O. D. E. type behavior of blow-up solutions of nonlinear heat equations. Zbl 1009.35039
Merle, Frank; Zaag, Hatem
9
2002
On blow up for the energy super critical defocusing nonlinear Schrödinger equations. Zbl 1487.35353
Merle, Frank; Raphaël, Pierre; Rodnianski, Igor; Szeftel, Jeremie
7
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
1
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
1
2022
On the implosion of a compressible fluid. II: Singularity formation. Zbl 1497.35385
Merle, Frank; Rapha\'’el, Pierre; Rodnianski, Igor; Szeftel, Jeremie
1
2022
Decay estimates for nonradiative solutions of the energy-critical focusing wave equation. Zbl 1472.35050
Duyckaerts, Thomas; Kenig, Carlos; Merle, Frank
2
2021
Strongly anisotropic type II blow up at an isolated point. Zbl 1436.35253
Collot, Charles; Merle, Frank; Raphaël, Pierre
12
2020
On strongly anisotropic type I blowup. Zbl 1432.35124
Merle, Frank; Raphaël, Pierre; Szeftel, Jeremie
8
2020
Exterior energy bounds for the critical wave equation close to the ground state. Zbl 1450.35157
Duyckaerts, Thomas; Kenig, Carlos; Merle, Frank
3
2020
Scattering profile for global solutions of the energy-critical wave equation. Zbl 1437.35497
Duyckaerts, Thomas; Kenig, Carlos E.; Merle, Frank
7
2019
Inelasticity of soliton collisions for the 5D energy critical wave equation. Zbl 1408.76111
Martel, Yvan; Merle, Frank
4
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
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
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
34
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
28
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
7
2017
Solutions of the focusing nonradial critical wave equation with the compactness property. Zbl 1348.35141
Duyckaerts, Thomas; Kenig, Carlos; Merle, Frank
23
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
Codimension one threshold manifold for the critical gKdV equation. Zbl 1336.35315
Martel, Yvan; Merle, Frank; Nakanishi, Kenji; Raphaël, Pierre
17
2016
Construction of multi-solitons for the energy-critical wave equation in dimension 5. Zbl 1359.35166
Martel, Yvan; Merle, Frank
17
2016
Concentration-compactness and universal profiles for the non-radial energy critical wave equation. Zbl 1339.35186
Duyckaerts, Thomas; Kenig, Carlos; Merle, Frank
12
2016
Global existence for solutions of the focusing wave equation with the compactness property. Zbl 1362.35190
Duyckaerts, Thomas; Kenig, Carlos; Merle, Frank
2
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
33
2015
Blow up for the critical gKdV equation. III: Exotic regimes. Zbl 1331.35307
Martel, Yvan; Merle, Frank; Raphaël, Pierre
31
2015
Blow up for the critical gKdV equation. II: Minimal mass dynamics. Zbl 1326.35320
Martel, Yvan; Merle, Frank; Raphaël, Pierre
29
2015
Type II blow up for the energy supercritical NLS. Zbl 1347.35215
Merle, Frank; Raphaël, Pierre; Rodnianski, Igor
22
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
11
2015
On the nonexistence of pure multi-solitons for the quartic gKdV equation. Zbl 1315.35191
Martel, Yvan; Merle, Frank
4
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
38
2014
Scattering for radial, bounded solutions of focusing supercritical wave equations. Zbl 1310.35171
Duyckaerts, Thomas; Kenig, Carlos; Merle, Frank
35
2014
On collapsing ring blow-up solutions to the mass supercritical nonlinear Schrödinger equation. Zbl 1292.35283
Merle, Frank; Raphaël, Pierre; Szeftel, Jeremie
14
2014
Near soliton dynamics and singularity formation for \( L^2\) critical problems. Zbl 1304.35650
Martel, Y.; Merle, F.; Raphaël, P.; Szeftel, J.
5
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
81
2013
Blowup dynamics for smooth data equivariant solutions to the critical Schrödinger map problem. Zbl 1326.35052
Merle, Frank; Raphaël, Pierre; Rodnianski, Igor
50
2013
The instability of Bourgain-Wang solutions for the \(L^2\) critical NLS. Zbl 1294.35145
Merle, Frank; Raphaël, Pierre; Szeftel, Jeremie
21
2013
Blow up and near soliton dynamics for the \(L^2\) critical gKdV equation. Zbl 1319.35224
Martel, Yvan; Merle, Frank; Raphaël, Pierre
5
2013
Profiles of bounded radial solutions of the focusing, energy-critical wave equation. Zbl 1258.35148
Duyckaerts, Thomas; Kenig, Carlos; Merle, Frank
57
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
54
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
41
2012
Isolatedness of characteristic points at blowup for a 1-dimensional semilinear wave equation. Zbl 1270.35320
Merle, Frank; Zaag, Hatem
26
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
86
2011
Construction of multi-soliton solutions for the \(L^2\)-supercritical gKdV and NLS equations. Zbl 1273.35234
Côte, Raphaël; Martel, Yvan; Merle, Frank
54
2011
Nondispersive radial solutions to energy supercritical non-linear wave equations, with applications. Zbl 1241.35136
Kenig, Carlos E.; Merle, Frank
45
2011
Description of two soliton collision for the quartic gKdV equation. Zbl 1300.37045
Martel, Yvan; Merle, Frank
32
2011
Threshold and generic type I behaviors for a supercritical nonlinear heat equation. Zbl 1223.35088
Matano, Hiroshi; Merle, Frank
30
2011
Inelastic interaction of nearly equal solitons for the quartic gKdV equation. Zbl 1230.35121
Martel, Yvan; Merle, Frank
24
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
19
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
Radial solutions to energy supercritical wave equations in odd dimensions. Zbl 1298.35119
Kenig, Carlos E.; Merle, Frank
18
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
Maximizers for the Strichartz norm for small solutions of mass-critical NLS. Zbl 1247.35142
Duyckaerts, Thomas; Merle, Frank; Roudenko, Svetlana
5
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
56
2010
Stable self-similar blow-up dynamics for slightly \(L^{2}\) super-critical NLS equations. Zbl 1204.35153
Merle, Frank; Raphaël, Pierre; Szeftel, Jeremie
20
2010
Description of the inelastic collision of two solitary waves for the BBM equation. Zbl 1200.35267
Martel, Yvan; Merle, Frank; Mizumachi, Tetsu
10
2010
Inelastic interaction of nearly equal solitons for the BBM equation. Zbl 1188.35165
Martel, Yvan; Merle, Frank
5
2010
Dynamic of threshold solutions for energy-critical NLS. Zbl 1232.35150
Duyckaerts, Thomas; Merle, Frank
62
2009
Classification of type I and type II behaviors for a supercritical nonlinear heat equation. Zbl 1178.35084
Matano, Hiroshi; Merle, Frank
57
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
224
2008
Dynamics of threshold solutions for energy-critical wave equation. Zbl 1159.35043
Duyckaerts, Thomas; Merle, Frank
55
2008
Asymptotic stability of solitons of the gKdV equations with general nonlinearity. Zbl 1153.35068
Martel, Yvan; Merle, Frank
41
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
38
2008
Blow up of the critical norm for some radial \(L^2\) super critical nonlinear Schrödinger equations. Zbl 1188.35182
Merle, Frank; Raphaël, Pierre
26
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
17
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
42
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
359
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
89
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
59
2006
Multi solitary waves for nonlinear Schrödinger equations. Zbl 1133.35093
Martel, Yvan; Merle, Frank
59
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
29
2006
Asymptotic stability and Liouville theorem for scalar viscous conservation laws in cylinders. Zbl 1105.35051
Kenig, Carlos E.; Merle, Frank
5
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
142
2005
Profiles and quantization of the blow up mass for critical nonlinear Schrödinger equation. Zbl 1062.35137
Merle, Frank; Raphaël, Pierre
80
2005
Asymptotic stability of solitons of the subcritical gKdV equations revisited. Zbl 1064.35171
Martel, Yvan; Merle, Frank
60
2005
Determination of the blow-up rate for a critical semilinear wave equation. Zbl 1136.35055
Merle, Frank; Zaag, Hatem
43
2005
On growth rate near the blowup surface for semilinear wave equations. Zbl 1160.35478
Merle, Frank; Zaag, Hatem
21
2005
On one blow up point solutions to the critical nonlinear Schrödinger equation. Zbl 1117.35075
Merle, Frank; Raphael, Pierre
9
2005
On universality of blow up profile for \(L^2\) critical nonlinear Schrödinger equation. Zbl 1067.35110
Merle, Frank; Raphaël, Pierre
110
2004
On nonexistence of type II blowup for a supercritical nonlinear heat equation. Zbl 1112.35098
Matano, Hiroshi; Merle, Frank
84
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
82
2003
Determination of the blow-up rate for the semilinear wave equation. Zbl 1052.35043
Merle, Frank; Zaag, Hatem
46
2003
\(L^2\) stability of solitons for KdV equation. Zbl 1022.35061
Merle, F.; Vega, L.
30
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
94
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
68
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
55
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
Asymptotic stability of solitons for subcritical generalized KdV equations. Zbl 0981.35073
Martel, Yvan; Merle, Frank
76
2001
Existence of blow-up solutions in the energy space for the critical generalized KdV equation. Zbl 0970.35128
Merle, Frank
69
2001
Instability of solitons for the critical generalized Korteweg-de Vries equation. Zbl 0985.35071
Martel, Y.; Merle, F.
64
2001
Optimal bounds on positive blow-up solutions for a semilinear wave equation. Zbl 0989.35090
Antonini, Christophe; Merle, Frank
22
2001
Self-focusing on bounded domains. Zbl 0980.35154
Fibich, Gadi; Merle, Frank
16
2001
Uniform blow-up estimates for nonlinear heat equations and applications. Zbl 1019.35044
Merle, Frank; Zaag, Hatem
1
2001
...and 38 more Documents
all top 5

Cited by 1,468 Authors

73 Merle, Frank
45 Zaag, Hatem
44 Martel, Yvan
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
18 Côte, Raphaël
18 Del Pino, Manuel A.
18 Ding, Yanheng
18 Schlag, Wilhelm
18 Zhao, Lifeng
17 Donninger, Roland
17 Mizoguchi, Noriko
17 Souplet, Philippe
17 Zheng, Jiqiang
16 Holmer, Justin
16 Tarantello, Gabriella
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 1,368 more Authors
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Cited in 248 Serials

150 Journal of Differential Equations
99 Journal of Functional Analysis
83 Calculus of Variations and Partial Differential Equations
81 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods
77 Journal of Mathematical Analysis and Applications
76 Communications in Mathematical Physics
64 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire
60 Communications in Partial Differential Equations
54 Discrete and Continuous Dynamical Systems
51 Transactions of the American Mathematical Society
45 Journal of Mathematical Physics
40 Archive for Rational Mechanics and Analysis
36 Communications on Pure and Applied Analysis
33 Mathematische Annalen
28 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 Chinese Annals of Mathematics. Series B
5 Asymptotic Analysis
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 Monatshefte für Mathematik
4 SIAM Journal on Numerical Analysis
4 SIAM Journal on Scientific Computing
4 Journal of Inequalities and Applications
4 Communications in Nonlinear Science and Numerical Simulation
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 148 more Serials
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Cited in 46 Fields

1,892 Partial differential equations (35-XX)
143 Dynamical systems and ergodic theory (37-XX)
127 Quantum theory (81-XX)
126 Global analysis, analysis on manifolds (58-XX)
123 Fluid mechanics (76-XX)
87 Differential geometry (53-XX)
71 Numerical analysis (65-XX)
58 Operator theory (47-XX)
53 Statistical mechanics, structure of matter (82-XX)
49 Calculus of variations and optimal control; optimization (49-XX)
42 Functional analysis (46-XX)
37 Optics, electromagnetic theory (78-XX)
36 Ordinary differential equations (34-XX)
27 Harmonic analysis on Euclidean spaces (42-XX)
23 Biology and other natural sciences (92-XX)
20 Mechanics of deformable solids (74-XX)
19 Real functions (26-XX)
14 Functions of a complex variable (30-XX)
13 Probability theory and stochastic processes (60-XX)
12 Mechanics of particles and systems (70-XX)
12 Relativity and gravitational theory (83-XX)
11 Potential theory (31-XX)
10 Systems theory; control (93-XX)
8 Integral equations (45-XX)
8 Astronomy and astrophysics (85-XX)
5 Special functions (33-XX)
4 Difference and functional equations (39-XX)
4 Classical thermodynamics, heat transfer (80-XX)
3 Several complex variables and analytic spaces (32-XX)
3 Statistics (62-XX)
2 History and biography (01-XX)
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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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