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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 Comptes Rendus de l’Académie des Sciences. Série I
8 IMRN. International Mathematics Research Notices
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
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 Annals of Mathematics. Second Series
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

134 Publications have been cited 4,839 times in 1,857 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
354
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
323
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
208
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
130
2005
Determination of blow-up solutions with minimal mass for nonlinear Schrödinger equations with critical power. Zbl 0808.35141
Merle, F.
107
1993
On universality of blow up profile for \(L^2\) critical nonlinear Schrödinger equation. Zbl 1067.35110
Merle, Frank; Raphaël, Pierre
104
2004
Construction of solutions with exactly k blow-up points for the Schrödinger equation with critical nonlinearity. Zbl 0707.35021
Merle, Frank
95
1990
Stability and asymptotic stability for subcritical gKdV equations. Zbl 1017.35098
Martel, Yvan; Merle, Frank; Tsai, Tai-Peng
87
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.
86
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
81
2006
On nonexistence of type II blowup for a supercritical nonlinear heat equation. Zbl 1112.35098
Matano, Hiroshi; Merle, Frank
80
2004
Classification of the radial solutions of the focusing, energy-critical wave equation. Zbl 1308.35143
Duyckaerts, Thomas; Kenig, Carlos; Merle, Frank
77
2013
Sharp upper bound on the blow-up rate for the critical nonlinear Schrödinger equation. Zbl 1061.35135
Merle, Frank; Raphaël, Pierre
76
2003
L\({}^ 2\) concentration of blow-up solutions for the nonlinear Schrödinger equation with critical power nonlinearity. Zbl 0722.35047
Merle, Frank; Tsutsumi, Yoshio
75
1990
Asymptotic stability of solitons for subcritical generalized KdV equations. Zbl 0981.35073
Martel, Yvan; Merle, Frank
75
2001
Profiles and quantization of the blow up mass for critical nonlinear Schrödinger equation. Zbl 1062.35137
Merle, Frank; Raphaël, Pierre
74
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
72
1997
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
69
2011
A Liouville theorem for the critical generalized Korteweg-de Vries equation. Zbl 0963.37058
Martel, Yvan; Merle, Frank
67
2000
Existence of blow-up solutions in the energy space for the critical generalized KdV equation. Zbl 0970.35128
Merle, Frank
66
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
65
2002
Instability of solitons for the critical generalized Korteweg-de Vries equation. Zbl 0985.35071
Martel, Y.; Merle, F.
59
2001
Asymptotic stability of solitons of the subcritical gKdV equations revisited. Zbl 1064.35171
Martel, Yvan; Merle, Frank
58
2005
Classification of type I and type II behaviors for a supercritical nonlinear heat equation. Zbl 1178.35084
Matano, Hiroshi; Merle, Frank
55
2009
Dynamic of threshold solutions for energy-critical NLS. Zbl 1232.35150
Duyckaerts, Thomas; Merle, Frank
55
2009
Existence of stationary states for nonlinear Dirac equations. Zbl 0696.35154
Merle, F.
54
1988
Multi solitary waves for nonlinear Schrödinger equations. Zbl 1133.35093
Martel, Yvan; Merle, Frank
52
2006
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
52
2002
Solution of a nonlinear heat equation with arbitrarily given blow-up points. Zbl 0785.35012
Merle, Frank
52
1992
Scattering for \(\dot {H}^{1/2}\) bounded solutions to the cubic, defocusing NLS in 3 dimensions. Zbl 1188.35180
Kenig, Carlos E.; Merle, Frank
51
2010
Dynamics of threshold solutions for energy-critical wave equation. Zbl 1159.35043
Duyckaerts, Thomas; Merle, Frank
51
2008
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
50
2006
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
50
2012
Quantization effects for \(-\Delta u=u(1-| u|^ 2)\) in \(\mathbb{R}^ 2\). Zbl 0809.35019
Brézis, Haïm; Merle, Frank; Rivière, Tristan
50
1994
Profiles of bounded radial solutions of the focusing, energy-critical wave equation. Zbl 1258.35148
Duyckaerts, Thomas; Kenig, Carlos; Merle, Frank
47
2012
Construction of multi-soliton solutions for the \(L^2\)-supercritical gKdV and NLS equations. Zbl 1273.35234
Côte, Raphaël; Martel, Yvan; Merle, Frank
47
2011
A Liouville theorem for vector-valued nonlinear heat equations and applications. Zbl 0939.35086
Merle, Frank; Zaag, Hatem
46
2000
Blowup dynamics for smooth data equivariant solutions to the critical Schrödinger map problem. Zbl 1326.35052
Merle, Frank; Raphaël, Pierre; Rodnianski, Igor
46
2013
Determination of the blow-up rate for the semilinear wave equation. Zbl 1052.35043
Merle, Frank; Zaag, Hatem
43
2003
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
42
1992
Nondispersive radial solutions to energy supercritical non-linear wave equations, with applications. Zbl 1241.35136
Kenig, Carlos E.; Merle, Frank
42
2011
Existence and universality of the blow-up profile for the semilinear wave equation in one space dimension. Zbl 1133.35070
Merle, Frank; Zaag, Hatem
41
2007
Existence of excited states for a nonlinear Dirac field. Zbl 0696.35158
Balabane, Mikhael; Cazenave, Thierry; Douady, Adrien; Merle, Frank
41
1988
Determination of the blow-up rate for a critical semilinear wave equation. Zbl 1136.35055
Merle, Frank; Zaag, Hatem
41
2005
Existence of self-similar blow-up solutions for Zakharov equation in dimension two. I. Zbl 0808.35137
Glangetas, L.; Merle, F.
40
1994
Asymptotic stability of solitons of the gKdV equations with general nonlinearity. Zbl 1153.35068
Martel, Yvan; Merle, Frank
39
2008
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
38
2012
Blow up for the critical generalized Korteweg-de Vries equation. I: Dynamics near the soliton. Zbl 1301.35137
Martel, Yvan; Merle, Frank; Raphaël, Pierre
36
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
36
1996
Optimal estimates for blowup rate and behavior for nonlinear heat equations. Zbl 0899.35044
Merle, Frank; Zaag, Hatem
35
1998
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
35
2008
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
Scattering for radial, bounded solutions of focusing supercritical wave equations. Zbl 1310.35171
Duyckaerts, Thomas; Kenig, Carlos; Merle, Frank
32
2014
Description of two soliton collision for the quartic gKdV equation. Zbl 1300.37045
Martel, Yvan; Merle, Frank
31
2011
Blow up for the critical gKdV equation. III: Exotic regimes. Zbl 1331.35307
Martel, Yvan; Merle, Frank; Raphaël, Pierre
30
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
30
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
\(L^2\) stability of solitons for KdV equation. Zbl 1022.35061
Merle, F.; Vega, L.
29
2003
Threshold and generic type I behaviors for a supercritical nonlinear heat equation. Zbl 1223.35088
Matano, Hiroshi; Merle, Frank
28
2011
Refined uniform estimates at blow-up and applications for nonlinear heat equations. Zbl 0926.35024
Merle, F.; Zaag, H.
28
1998
Blow up for the critical gKdV equation. II: Minimal mass dynamics. Zbl 1326.35320
Martel, Yvan; Merle, Frank; Raphaël, Pierre
27
2015
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
27
2006
Positive solutions of elliptic equations involving supercritical growth. Zbl 0742.35025
Merle, F.; Peletier, L. A.
26
1991
Blow-up results of virial type for Zakharov equations. Zbl 0858.35117
Merle, Frank
25
1996
Isolatedness of characteristic points at blowup for a 1-dimensional semilinear wave equation. Zbl 1270.35320
Merle, Frank; Zaag, Hatem
25
2012
Dynamics near the ground state for the energy critical nonlinear heat equation in large dimensions. Zbl 1401.35178
Collot, Charles; Merle, Frank; Raphaël, Pierre
25
2017
Blow up of the critical norm for some radial \(L^2\) super critical nonlinear Schrödinger equations. Zbl 1188.35182
Merle, Frank; Raphaël, Pierre
23
2008
Solutions of the focusing nonradial critical wave equation with the compactness property. Zbl 1348.35141
Duyckaerts, Thomas; Kenig, Carlos; Merle, Frank
22
2016
Optimal bounds on positive blow-up solutions for a semilinear wave equation. Zbl 0989.35090
Antonini, Christophe; Merle, Frank
22
2001
Inelastic interaction of nearly equal solitons for the quartic gKdV equation. Zbl 1230.35121
Martel, Yvan; Merle, Frank
21
2011
Stability of two soliton collision for nonintegrable gKdV equations. Zbl 1179.35291
Martel, Yvan; Merle, Frank
21
2009
Nonexistence of blow-up solution with minimal \(L^2\)-mass for the critical gKdV equation. Zbl 1033.35102
Martel, Yvan; Merle, Frank
21
2002
On growth rate near the blowup surface for semilinear wave equations. Zbl 1160.35478
Merle, Frank; Zaag, Hatem
21
2005
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
Type II blow up for the energy supercritical NLS. Zbl 1347.35215
Merle, Frank; Raphaël, Pierre; Rodnianski, Igor
19
2015
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
Limit of the solution of a nonlinear Schrödinger equation at blow-up time. Zbl 0681.35078
Merle, F.
18
1989
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
17
2011
Codimension one threshold manifold for the critical gKdV equation. Zbl 1336.35315
Martel, Yvan; Merle, Frank; Nakanishi, Kenji; Raphaël, Pierre
17
2016
The instability of Bourgain-Wang solutions for the \(L^2\) critical NLS. Zbl 1294.35145
Merle, Frank; Raphaël, Pierre; Szeftel, Jeremie
17
2013
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
16
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.
16
1992
Blow-up behavior outside the origin for a semilinear wave equation in the radial case. Zbl 1222.35126
Merle, Frank; Zaag, Hatem
16
2011
Radial solutions to energy supercritical wave equations in odd dimensions. Zbl 1298.35119
Kenig, Carlos E.; Merle, Frank
16
2011
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
16
2008
Self-focusing on bounded domains. Zbl 0980.35154
Fibich, Gadi; Merle, Frank
15
2001
Construction of multi-solitons for the energy-critical wave equation in dimension 5. Zbl 1359.35166
Martel, Yvan; Merle, Frank
14
2016
On collapsing ring blow-up solutions to the mass supercritical nonlinear Schrödinger equation. Zbl 1292.35283
Merle, Frank; Raphaël, Pierre; Szeftel, Jeremie
13
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
12
1997
Modulation theory for the blowup of vector-valued nonlinear heat equations. Zbl 0814.35043
Filippas, Stathis; Merle, Frank
12
1995
Refined asymptotics around solitons for gKdV equations. Zbl 1137.35062
Martel, Yvan; Merle, Frank
12
2008
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
Concentration-compactness and universal profiles for the non-radial energy critical wave equation. Zbl 1339.35186
Duyckaerts, Thomas; Kenig, Carlos; Merle, Frank
11
2016
Description of the inelastic collision of two solitary waves for the BBM equation. Zbl 1200.35267
Martel, Yvan; Merle, Frank; Mizumachi, Tetsu
9
2010
Limit behavior of saturated approximations of nonlinear Schrödinger equation. Zbl 0756.35094
Merle, F.
9
1992
O. D. E. type behavior of blow-up solutions of nonlinear heat equations. Zbl 1009.35039
Merle, Frank; Zaag, Hatem
9
2002
On one blow up point solutions to the critical nonlinear Schrödinger equation. Zbl 1117.35075
Merle, Frank; Raphael, Pierre
8
2005
Strongly anisotropic type II blow up at an isolated point. Zbl 1436.35253
Collot, Charles; Merle, Frank; Raphaël, Pierre
8
2020
On blow up for the energy super critical defocusing nonlinear Schrödinger equations. Zbl 07470584
Merle, Frank; Raphaël, 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
1
2021
Strongly anisotropic type II blow up at an isolated point. Zbl 1436.35253
Collot, Charles; Merle, Frank; Raphaël, Pierre
8
2020
On strongly anisotropic type I blowup. Zbl 1432.35124
Merle, Frank; Raphaël, Pierre; Szeftel, Jeremie
3
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
5
2019
Inelasticity of soliton collisions for the 5D energy critical wave equation. Zbl 1408.76111
Martel, Yvan; Merle, Frank
3
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
Blowup solutions to the semilinear wave equation with a stylized pyramid as a blowup surface. Zbl 1402.35181
Merle, Frank; Zaag, Hatem
1
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
25
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
6
2017
Solutions of the focusing nonradial critical wave equation with the compactness property. Zbl 1348.35141
Duyckaerts, Thomas; Kenig, Carlos; Merle, Frank
22
2016
Codimension one threshold manifold for the critical gKdV equation. Zbl 1336.35315
Martel, Yvan; Merle, Frank; Nakanishi, Kenji; Raphaël, Pierre
17
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
16
2016
Construction of multi-solitons for the energy-critical wave equation in dimension 5. Zbl 1359.35166
Martel, Yvan; Merle, Frank
14
2016
Concentration-compactness and universal profiles for the non-radial energy critical wave equation. Zbl 1339.35186
Duyckaerts, Thomas; Kenig, Carlos; Merle, Frank
11
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
Blow up for the critical gKdV equation. III: Exotic regimes. Zbl 1331.35307
Martel, Yvan; Merle, Frank; Raphaël, Pierre
30
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
30
2015
Blow up for the critical gKdV equation. II: Minimal mass dynamics. Zbl 1326.35320
Martel, Yvan; Merle, Frank; Raphaël, Pierre
27
2015
Type II blow up for the energy supercritical NLS. Zbl 1347.35215
Merle, Frank; Raphaël, Pierre; Rodnianski, Igor
19
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
36
2014
Scattering for radial, bounded solutions of focusing supercritical wave equations. Zbl 1310.35171
Duyckaerts, Thomas; Kenig, Carlos; Merle, Frank
32
2014
On collapsing ring blow-up solutions to the mass supercritical nonlinear Schrödinger equation. Zbl 1292.35283
Merle, Frank; Raphaël, Pierre; Szeftel, Jeremie
13
2014
Near soliton dynamics and singularity formation for \( L^2\) critical problems. Zbl 1304.35650
Martel, Y.; Merle, F.; Raphaël, P.; Szeftel, J.
4
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
77
2013
Blowup dynamics for smooth data equivariant solutions to the critical Schrödinger map problem. Zbl 1326.35052
Merle, Frank; Raphaël, Pierre; Rodnianski, Igor
46
2013
The instability of Bourgain-Wang solutions for the \(L^2\) critical NLS. Zbl 1294.35145
Merle, Frank; Raphaël, Pierre; Szeftel, Jeremie
17
2013
Blow up and near soliton dynamics for the \(L^2\) critical gKdV equation. Zbl 1319.35224
Martel, Yvan; Merle, Frank; Raphaël, Pierre
4
2013
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
50
2012
Profiles of bounded radial solutions of the focusing, energy-critical wave equation. Zbl 1258.35148
Duyckaerts, Thomas; Kenig, Carlos; Merle, Frank
47
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
38
2012
Isolatedness of characteristic points at blowup for a 1-dimensional semilinear wave equation. Zbl 1270.35320
Merle, Frank; Zaag, Hatem
25
2012
Isolatedness of characteristic points at blow-up for a semilinear wave equation in one space dimension. Zbl 1280.35019
Merle, Frank
2
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
69
2011
Construction of multi-soliton solutions for the \(L^2\)-supercritical gKdV and NLS equations. Zbl 1273.35234
Côte, Raphaël; Martel, Yvan; Merle, Frank
47
2011
Nondispersive radial solutions to energy supercritical non-linear wave equations, with applications. Zbl 1241.35136
Kenig, Carlos E.; Merle, Frank
42
2011
Description of two soliton collision for the quartic gKdV equation. Zbl 1300.37045
Martel, Yvan; Merle, Frank
31
2011
Threshold and generic type I behaviors for a supercritical nonlinear heat equation. Zbl 1223.35088
Matano, Hiroshi; Merle, Frank
28
2011
Inelastic interaction of nearly equal solitons for the quartic gKdV equation. Zbl 1230.35121
Martel, Yvan; Merle, Frank
21
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
17
2011
Blow-up behavior outside the origin for a semilinear wave equation in the radial case. Zbl 1222.35126
Merle, Frank; Zaag, Hatem
16
2011
Radial solutions to energy supercritical wave equations in odd dimensions. Zbl 1298.35119
Kenig, Carlos E.; Merle, Frank
16
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
51
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
9
2010
Inelastic interaction of nearly equal solitons for the BBM equation. Zbl 1188.35165
Martel, Yvan; Merle, Frank
4
2010
Classification of type I and type II behaviors for a supercritical nonlinear heat equation. Zbl 1178.35084
Matano, Hiroshi; Merle, Frank
55
2009
Dynamic of threshold solutions for energy-critical NLS. Zbl 1232.35150
Duyckaerts, Thomas; Merle, Frank
55
2009
Stability of two soliton collision for nonintegrable gKdV equations. Zbl 1179.35291
Martel, Yvan; Merle, Frank
21
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
208
2008
Dynamics of threshold solutions for energy-critical wave equation. Zbl 1159.35043
Duyckaerts, Thomas; Merle, Frank
51
2008
Asymptotic stability of solitons of the gKdV equations with general nonlinearity. Zbl 1153.35068
Martel, Yvan; Merle, Frank
39
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
35
2008
Blow up of the critical norm for some radial \(L^2\) super critical nonlinear Schrödinger equations. Zbl 1188.35182
Merle, Frank; Raphaël, Pierre
23
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
16
2008
Refined asymptotics around solitons for gKdV equations. Zbl 1137.35062
Martel, Yvan; Merle, Frank
12
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
41
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
323
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
81
2006
Multi solitary waves for nonlinear Schrödinger equations. Zbl 1133.35093
Martel, Yvan; Merle, Frank
52
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
50
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
27
2006
Asymptotic stability and Liouville theorem for scalar viscous conservation laws in cylinders. Zbl 1105.35051
Kenig, Carlos E.; Merle, Frank
4
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
130
2005
Profiles and quantization of the blow up mass for critical nonlinear Schrödinger equation. Zbl 1062.35137
Merle, Frank; Raphaël, Pierre
74
2005
Asymptotic stability of solitons of the subcritical gKdV equations revisited. Zbl 1064.35171
Martel, Yvan; Merle, Frank
58
2005
Determination of the blow-up rate for a critical semilinear wave equation. Zbl 1136.35055
Merle, Frank; Zaag, Hatem
41
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
8
2005
On universality of blow up profile for \(L^2\) critical nonlinear Schrödinger equation. Zbl 1067.35110
Merle, Frank; Raphaël, Pierre
104
2004
On nonexistence of type II blowup for a supercritical nonlinear heat equation. Zbl 1112.35098
Matano, Hiroshi; Merle, Frank
80
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
76
2003
Determination of the blow-up rate for the semilinear wave equation. Zbl 1052.35043
Merle, Frank; Zaag, Hatem
43
2003
\(L^2\) stability of solitons for KdV equation. Zbl 1022.35061
Merle, F.; Vega, L.
29
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
87
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
65
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
52
2002
Nonexistence of blow-up solution with minimal \(L^2\)-mass for the critical gKdV equation. Zbl 1033.35102
Martel, Yvan; Merle, Frank
21
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
75
2001
Existence of blow-up solutions in the energy space for the critical generalized KdV equation. Zbl 0970.35128
Merle, Frank
66
2001
Instability of solitons for the critical generalized Korteweg-de Vries equation. Zbl 0985.35071
Martel, Y.; Merle, F.
59
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
15
2001
Uniform blow-up estimates for nonlinear heat equations and applications. Zbl 1019.35044
Merle, Frank; Zaag, Hatem
1
2001
A Liouville theorem for the critical generalized Korteweg-de Vries equation. Zbl 0963.37058
Martel, Yvan; Merle, Frank
67
2000
A Liouville theorem for vector-valued nonlinear heat equations and applications. Zbl 0939.35086
Merle, Frank; Zaag, Hatem
46
2000
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
Compactness at blow-up time for \(L^2\) solutions of the critical nonlinear Schrödinger equation in 2D. Zbl 0913.35126
Merle, F.; Vega, L.
86
1998
...and 34 more Documents
all top 5

Cited by 1,385 Authors

71 Merle, Frank
44 Martel, Yvan
42 Zaag, Hatem
41 Wei, Juncheng
38 Raphael, Pierre
34 Kenig, Carlos Eduardo
31 Bartolucci, Daniele
29 Lin, Chang-Shou
28 Muñoz, Claudio
25 Musso, Monica
22 Krieger, Joachim
21 Duyckaerts, Thomas
20 Saanouni, Tarek
18 Côte, Raphaël
18 Del Pino, Manuel A.
18 Ding, Yanheng
18 Schlag, Wilhelm
18 Zhao, Lifeng
17 Donninger, Roland
17 Miao, Changxing
17 Roudenko, Svetlana
16 Mizoguchi, Noriko
16 Souplet, Philippe
16 Tarantello, Gabriella
16 Zhang, Jian
16 Zhu, Shihui
15 Dinh, Van Duong
15 Guo, Boling
15 Holmer, Justin
15 Martinazzi, Luca
15 Nakanishi, Kenji
15 Visan, Monica
15 Zheng, Jiqiang
15 Zhou, Chunqin
14 Lee, Youngae
14 Yang, Wen
13 Malchiodi, Andrea
13 Suzuki, Takashi
13 Tataru, Daniel
12 Dodson, Benjamin G.
12 Farah, Luiz Gustavo
12 Killip, Rowan
12 Wang, Guofang
12 Xu, Guixiang
12 Zhang, Xiaoyi
11 Bahouri, Hajer
11 Ibrahim, Slim
11 Jevnikar, Aleks
11 Jost, Jürgen
11 Lawrie, Andrew G. W.
11 Murphy, Jason
11 Nguyen, Van Tien
10 Cazenave, Thierry
10 Cuccagna, Scipio
10 Kowalczyk, Michał
9 Carles, Rémi
9 Fibich, Gadi
9 Ghoul, Tej-Eddine
9 Hamza, Mohamed Ali
9 Jendrej, Jacek
9 Li, Dong
9 Miyamoto, Yasuhito
9 Pistoia, Angela
9 Yang, Kai
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 Liu, Yue
8 Maeda, Masaya
8 Masmoudi, Nader
8 Pausader, Benoît
8 Perelman, Galina
8 Struwe, Michael
8 Tao, Terence
8 Tzvetkov, Nikolay
8 Zhang, Lei
7 Banica, Valeria
7 Cheng, Xing
7 Cho, Yonggeun
7 Choe, Kwangseok
7 Collot, Charles
7 Forcella, Luigi
7 Galaktionov, Victor Aleksandrovich
7 Guo, Qing
7 Ishige, Kazuhiro
7 Keraani, Sahbi
7 Kikuchi, Hiroaki
7 Lucia, Marcello
7 Mizumachi, Tetsu
7 Nawa, Hayato
7 Pastor, Ademir
7 Ponce, Gustavo
...and 1,285 more Authors
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Cited in 233 Serials

147 Journal of Differential Equations
93 Journal of Functional Analysis
76 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods
76 Calculus of Variations and Partial Differential Equations
74 Communications in Mathematical Physics
74 Journal of Mathematical Analysis and Applications
64 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire
60 Communications in Partial Differential Equations
52 Discrete and Continuous Dynamical Systems
49 Transactions of the American Mathematical Society
44 Journal of Mathematical Physics
37 Archive for Rational Mechanics and Analysis
35 Communications on Pure and Applied Analysis
33 Mathematische Annalen
25 Duke Mathematical Journal
25 Physica D
25 Journal de Mathématiques Pures et Appliquées. Neuvième Série
25 Communications in Contemporary Mathematics
23 Proceedings of the American Mathematical Society
23 SIAM Journal on Mathematical Analysis
22 Advances in Mathematics
22 Séminaire Laurent Schwartz. EDP et Applications
20 Nonlinearity
20 Acta Mathematica Sinica. English Series
19 Inventiones Mathematicae
18 Journal of Evolution Equations
18 Journal of Hyperbolic Differential Equations
17 Communications on Pure and Applied Mathematics
17 Comptes Rendus. Mathématique. Académie des Sciences, Paris
16 NoDEA. Nonlinear Differential Equations and Applications
14 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics
13 Applicable Analysis
13 Journal of the European Mathematical Society (JEMS)
13 Annals of PDE
12 Science China. Mathematics
11 Journal d’Analyse Mathématique
11 ZAMP. Zeitschrift für angewandte Mathematik und Physik
11 Journal of the American Mathematical Society
11 Journal of Dynamics and Differential Equations
11 Analysis & PDE
9 Annali di Matematica Pura ed Applicata. Serie Quarta
9 Nonlinear Analysis. Real World Applications
9 Nonlinear Analysis. Theory, Methods & Applications
8 Mathematical Methods in the Applied Sciences
8 Applied Mathematics and Computation
8 Revista Matemática Iberoamericana
8 The Journal of Geometric Analysis
8 Journal of Nonlinear Science
8 Advanced Nonlinear Studies
7 Applied Mathematics Letters
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 Discrete and Continuous Dynamical Systems. Series B
6 Journal of Computational Physics
6 Mathematische Zeitschrift
6 Memoirs of the American Mathematical Society
6 Bulletin of the American Mathematical Society. New Series
6 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V
6 Boundary Value Problems
6 Discrete and Continuous Dynamical Systems. Series S
5 Reviews in Mathematical Physics
5 Indiana University Mathematics Journal
5 Manuscripta Mathematica
5 Chinese Annals of Mathematics. Series B
5 Milan Journal of Mathematics
5 Advances in Nonlinear Analysis
4 Computers & Mathematics with Applications
4 Annales de l’Institut Fourier
4 Journal of Computational and Applied Mathematics
4 Journal of Inequalities and Applications
4 Annals of Mathematics. Second Series
4 Communications in Nonlinear Science and Numerical Simulation
4 Communications in Mathematics and Statistics
4 Journal of Elliptic and Parabolic Equations
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 Illinois Journal of Mathematics
3 Journal of the Korean Mathematical Society
3 Journal für die Reine und Angewandte Mathematik
3 Monatshefte für Mathematik
3 Proceedings of the Edinburgh Mathematical Society. Series II
3 Proceedings of the London Mathematical Society. Third Series
3 SIAM Journal on Numerical Analysis
3 Acta Applicandae Mathematicae
3 Asymptotic Analysis
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
3 Journal of Fixed Point Theory and Applications
3 Frontiers of Mathematics in China
3 Kyoto Journal of Mathematics
3 Evolution Equations and Control Theory
3 SN Partial Differential Equations and Applications
2 Journal of Statistical Physics
...and 133 more Serials
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Cited in 47 Fields

1,765 Partial differential equations (35-XX)
130 Dynamical systems and ergodic theory (37-XX)
119 Global analysis, analysis on manifolds (58-XX)
118 Quantum theory (81-XX)
112 Fluid mechanics (76-XX)
84 Differential geometry (53-XX)
63 Numerical analysis (65-XX)
51 Operator theory (47-XX)
51 Statistical mechanics, structure of matter (82-XX)
45 Calculus of variations and optimal control; optimization (49-XX)
40 Functional analysis (46-XX)
35 Optics, electromagnetic theory (78-XX)
33 Ordinary differential equations (34-XX)
22 Harmonic analysis on Euclidean spaces (42-XX)
21 Biology and other natural sciences (92-XX)
19 Real functions (26-XX)
19 Mechanics of deformable solids (74-XX)
13 Probability theory and stochastic processes (60-XX)
12 Functions of a complex variable (30-XX)
11 Mechanics of particles and systems (70-XX)
11 Relativity and gravitational theory (83-XX)
9 Systems theory; control (93-XX)
8 Integral equations (45-XX)
7 Potential theory (31-XX)
6 Astronomy and astrophysics (85-XX)
5 Special functions (33-XX)
5 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)
2 Linear and multilinear algebra; matrix theory (15-XX)
2 Nonassociative rings and algebras (17-XX)
2 Measure and integration (28-XX)
2 Geophysics (86-XX)
1 General and overarching topics; collections (00-XX)
1 Field theory and polynomials (12-XX)
1 Algebraic geometry (14-XX)
1 Category theory; homological algebra (18-XX)
1 Group theory and generalizations (20-XX)
1 Topological groups, Lie groups (22-XX)
1 Approximations and expansions (41-XX)
1 Abstract harmonic analysis (43-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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