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Merle, Frank

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Author ID: merle.frank Recent zbMATH articles by "Merle, Frank"
Published as: Merle, F.; Merle, Franck; Merle, Frank
Homepage: https://www.ihes.fr/en/professeur/frank-merle-2/
External Links: MGP · Math-Net.Ru · Wikidata · ResearchGate · dblp
Documents Indexed: 156 Publications since 1987, including 4 Books
all top 5

Serials

15 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
5 American Journal of Mathematics
5 Inventiones Mathematicae
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
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 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
1 Séminaire Laurent Schwartz. EDP et Applications

Publications by Year

Citations contained in zbMATH

131 Publications have been cited 4,183 times in 1,609 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
320
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
260
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
172
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
109
2005
On universality of blow up profile for \(L^2\) critical nonlinear Schrödinger equation. Zbl 1067.35110
Merle, Frank; Raphaël, Pierre
95
2004
Determination of blow-up solutions with minimal mass for nonlinear Schrödinger equations with critical power. Zbl 0808.35141
Merle, F.
94
1993
Construction of solutions with exactly k blow-up points for the Schrödinger equation with critical nonlinearity. Zbl 0707.35021
Merle, Frank
84
1990
Compactness at blow-up time for \(L^2\) solutions of the critical nonlinear Schrödinger equation in 2D. Zbl 0913.35126
Merle, F.; Vega, L.
78
1998
L\({}^ 2\) concentration of blow-up solutions for the nonlinear Schrödinger equation with critical power nonlinearity. Zbl 0722.35047
Merle, Frank; Tsutsumi, Yoshio
74
1990
On nonexistence of type II blowup for a supercritical nonlinear heat equation. Zbl 1112.35098
Matano, Hiroshi; Merle, Frank
72
2004
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
68
2006
Profiles and quantization of the blow up mass for critical nonlinear Schrödinger equation. Zbl 1062.35137
Merle, Frank; Raphaël, Pierre
68
2005
Stability and asymptotic stability for subcritical gKdV equations. Zbl 1017.35098
Martel, Yvan; Merle, Frank; Tsai, Tai-Peng
68
2002
Sharp upper bound on the blow-up rate for the critical nonlinear Schrödinger equation. Zbl 1061.35135
Merle, Frank; Raphaël, Pierre
67
2003
Asymptotic stability of solitons for subcritical generalized KdV equations. Zbl 0981.35073
Martel, Yvan; Merle, Frank
63
2001
Classification of the radial solutions of the focusing, energy-critical wave equation. Zbl 1308.35143
Duyckaerts, Thomas; Kenig, Carlos; Merle, Frank
60
2013
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
58
2011
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
58
1997
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
56
2002
A Liouville theorem for the critical generalized Korteweg-de Vries equation. Zbl 0963.37058
Martel, Yvan; Merle, Frank
56
2000
Existence of blow-up solutions in the energy space for the critical generalized KdV equation. Zbl 0970.35128
Merle, Frank
54
2001
Optimal estimates for blowup rate and behavior for nonlinear heat equations. Zbl 0899.35044
Merle, Frank; Zaag, Hatem
54
1998
Classification of type I and type II behaviors for a supercritical nonlinear heat equation. Zbl 1178.35084
Matano, Hiroshi; Merle, Frank
50
2009
Asymptotic stability of solitons of the subcritical gKdV equations revisited. Zbl 1064.35171
Martel, Yvan; Merle, Frank
50
2005
Solution of a nonlinear heat equation with arbitrarily given blow-up points. Zbl 0785.35012
Merle, Frank
49
1992
Existence of stationary states for nonlinear Dirac equations. Zbl 0696.35154
Merle, F.
48
1988
Dynamic of threshold solutions for energy-critical NLS. Zbl 1232.35150
Duyckaerts, Thomas; Merle, Frank
47
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
47
2002
Instability of solitons for the critical generalized Korteweg-de Vries equation. Zbl 0985.35071
Martel, Y.; Merle, F.
47
2001
Quantization effects for \(-\Delta u=u(1-| u|^ 2)\) in \(\mathbb{R}^ 2\). Zbl 0809.35019
Brézis, Haïm; Merle, Frank; Rivière, Tristan
47
1994
Dynamics of threshold solutions for energy-critical wave equation. Zbl 1159.35043
Duyckaerts, Thomas; Merle, Frank
46
2008
Scattering for \(\dot {H}^{1/2}\) bounded solutions to the cubic, defocusing NLS in 3 dimensions. Zbl 1188.35180
Kenig, Carlos E.; Merle, Frank
45
2010
Profiles of bounded radial solutions of the focusing, energy-critical wave equation. Zbl 1258.35148
Duyckaerts, Thomas; Kenig, Carlos; Merle, Frank
43
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
43
2012
A Liouville theorem for vector-valued nonlinear heat equations and applications. Zbl 0939.35086
Merle, Frank; Zaag, Hatem
43
2000
Multi solitary waves for nonlinear Schrödinger equations. Zbl 1133.35093
Martel, Yvan; Merle, Frank
41
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
40
2006
Nondispersive radial solutions to energy supercritical non-linear wave equations, with applications. Zbl 1241.35136
Kenig, Carlos E.; Merle, Frank
39
2011
Determination of the blow-up rate for the semilinear wave equation. Zbl 1052.35043
Merle, Frank; Zaag, Hatem
38
2003
Blowup dynamics for smooth data equivariant solutions to the critical Schrödinger map problem. Zbl 1326.35052
Merle, Frank; Raphaël, Pierre; Rodnianski, Igor
37
2013
Determination of the blow-up rate for a critical semilinear wave equation. Zbl 1136.35055
Merle, Frank; Zaag, Hatem
37
2005
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
37
1992
Existence of excited states for a nonlinear Dirac field. Zbl 0696.35158
Balabane, Mikhael; Cazenave, Thierry; Douady, Adrien; Merle, Frank
36
1988
Existence and universality of the blow-up profile for the semilinear wave equation in one space dimension. Zbl 1133.35070
Merle, Frank; Zaag, Hatem
35
2007
Existence of self-similar blow-up solutions for Zakharov equation in dimension two. I. Zbl 0808.35137
Glangetas, L.; Merle, F.
35
1994
Construction of multi-soliton solutions for the \(L^2\)-supercritical gKdV and NLS equations. Zbl 1273.35234
Côte, Raphaël; Martel, Yvan; Merle, Frank
33
2011
Concentration properties of blow-up solutions and instability results for Zakharov equation in dimension two. II. Zbl 0808.35138
Glangetas, L.; Merle, F.
33
1994
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
32
2012
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
32
1996
Asymptotic stability of solitons of the gKdV equations with general nonlinearity. Zbl 1153.35068
Martel, Yvan; Merle, Frank
31
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
30
2008
Description of two soliton collision for the quartic gKdV equation. Zbl 1300.37045
Martel, Yvan; Merle, Frank
28
2011
Scattering for radial, bounded solutions of focusing supercritical wave equations. Zbl 1310.35171
Duyckaerts, Thomas; Kenig, Carlos; Merle, Frank
27
2014
Blow up for the critical generalized Korteweg-de Vries equation. I: Dynamics near the soliton. Zbl 1301.35137
Martel, Yvan; Merle, Frank; Raphaël, Pierre
27
2014
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.
27
2000
Blow up for the critical gKdV equation. III: Exotic regimes. Zbl 1331.35307
Martel, Yvan; Merle, Frank; Raphaël, Pierre
26
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
25
2006
\(L^2\) stability of solitons for KdV equation. Zbl 1022.35061
Merle, F.; Vega, L.
25
2003
Refined uniform estimates at blow-up and applications for nonlinear heat equations. Zbl 0926.35024
Merle, F.; Zaag, H.
25
1998
Threshold and generic type I behaviors for a supercritical nonlinear heat equation. Zbl 1223.35088
Matano, Hiroshi; Merle, Frank
24
2011
Positive solutions of elliptic equations involving supercritical growth. Zbl 0742.35025
Merle, F.; Peletier, L. A.
24
1991
Blow up for the critical gKdV equation. II: Minimal mass dynamics. Zbl 1326.35320
Martel, Yvan; Merle, Frank; Raphaël, Pierre
22
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
22
2015
On growth rate near the blowup surface for semilinear wave equations. Zbl 1160.35478
Merle, Frank; Zaag, Hatem
22
2005
Blow-up results of virial type for Zakharov equations. Zbl 0858.35117
Merle, Frank
22
1996
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
21
2017
Stability of two soliton collision for nonintegrable gKdV equations. Zbl 1179.35291
Martel, Yvan; Merle, Frank
21
2009
Isolatedness of characteristic points at blowup for a 1-dimensional semilinear wave equation. Zbl 1270.35320
Merle, Frank; Zaag, Hatem
20
2012
Optimal bounds on positive blow-up solutions for a semilinear wave equation. Zbl 0989.35090
Antonini, Christophe; Merle, Frank
20
2001
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.
20
1990
Blow up of the critical norm for some radial \(L^2\) super critical nonlinear Schrödinger equations. Zbl 1188.35182
Merle, Frank; Raphaël, Pierre
19
2008
Dynamics near the ground state for the energy critical nonlinear heat equation in large dimensions. Zbl 1401.35178
Collot, Charles; Merle, Frank; Raphaël, Pierre
18
2017
Inelastic interaction of nearly equal solitons for the quartic gKdV equation. Zbl 1230.35121
Martel, Yvan; Merle, Frank
18
2011
Nonexistence of blow-up solution with minimal \(L^2\)-mass for the critical gKdV equation. Zbl 1033.35102
Martel, Yvan; Merle, Frank
18
2002
Stable self-similar blow-up dynamics for slightly \(L^{2}\) super-critical NLS equations. Zbl 1204.35153
Merle, Frank; Raphaël, Pierre; Szeftel, Jeremie
17
2010
Limit of the solution of a nonlinear Schrödinger equation at blow-up time. Zbl 0681.35078
Merle, F.
17
1989
Type II blow up for the energy supercritical NLS. Zbl 1347.35215
Merle, Frank; Raphaël, Pierre; Rodnianski, Igor
16
2015
Blow up dynamics for smooth equivariant solutions to the energy critical Schrödinger map. Zbl 1213.35139
Merle, Frank; Raphaël, Pierre; Rodnianski, Igor
16
2011
Solutions of the focusing nonradial critical wave equation with the compactness property. Zbl 1348.35141
Duyckaerts, Thomas; Kenig, Carlos; Merle, Frank
15
2016
Radial solutions to energy supercritical wave equations in odd dimensions. Zbl 1298.35119
Kenig, Carlos E.; Merle, Frank
15
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
15
2008
Self-focusing on bounded domains. Zbl 0980.35154
Fibich, Gadi; Merle, Frank
15
2001
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.
15
1992
Blow-up behavior outside the origin for a semilinear wave equation in the radial case. Zbl 1222.35126
Merle, Frank; Zaag, Hatem
14
2011
Codimension one threshold manifold for the critical gKdV equation. Zbl 1336.35315
Martel, Yvan; Merle, Frank; Nakanishi, Kenji; Raphaël, Pierre
13
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
13
2016
The instability of Bourgain-Wang solutions for the \(L^2\) critical NLS. Zbl 1294.35145
Merle, Frank; Raphaël, Pierre; Szeftel, Jeremie
13
2013
Modulation theory for the blowup of vector-valued nonlinear heat equations. Zbl 0814.35043
Filippas, Stathis; Merle, Frank
13
1995
Lower bounds for the blowup rate of solutions of the Zakharov equation in dimension two. Zbl 0856.35014
Merle, Frank
12
1996
Construction of multi-solitons for the energy-critical wave equation in dimension 5. Zbl 1359.35166
Martel, Yvan; Merle, Frank
11
2016
Refined asymptotics around solitons for gKdV equations. Zbl 1137.35062
Martel, Yvan; Merle, Frank
11
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
10
2015
Reconnection of vortex with the boundary and finite time quenching. Zbl 0910.35020
Merle, Frank; Zaag, Hatem
10
1997
Concentration-compactness and universal profiles for the non-radial energy critical wave equation. Zbl 1339.35186
Duyckaerts, Thomas; Kenig, Carlos; Merle, Frank
9
2016
On collapsing ring blow-up solutions to the mass supercritical nonlinear Schrödinger equation. Zbl 1292.35283
Merle, Frank; Raphaël, Pierre; Szeftel, Jeremie
9
2014
Description of the inelastic collision of two solitary waves for the BBM equation. Zbl 1200.35267
Martel, Yvan; Merle, Frank; Mizumachi, Tetsu
9
2010
On one blow up point solutions to the critical nonlinear Schrödinger equation. Zbl 1117.35075
Merle, Frank; Raphael, Pierre
8
2005
O. D. E. type behavior of blow-up solutions of nonlinear heat equations. Zbl 1009.35039
Merle, Frank; Zaag, Hatem
8
2002
Limit behavior of saturated approximations of nonlinear Schrödinger equation. Zbl 0756.35094
Merle, F.
7
1992
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
Strongly anisotropic type II blow up at an isolated point. Zbl 1436.35253
Collot, Charles; Merle, Frank; Raphaël, Pierre
2
2020
Exterior energy bounds for the critical wave equation close to the ground state. Zbl 1450.35157
Duyckaerts, Thomas; Kenig, Carlos; Merle, Frank
1
2020
On strongly anisotropic type I blowup. Zbl 1432.35124
Merle, Frank; Raphaël, Pierre; Szeftel, Jeremie
1
2020
Scattering profile for global solutions of the energy-critical wave equation. Zbl 1437.35497
Duyckaerts, Thomas; Kenig, Carlos E.; Merle, Frank
2
2019
Inelasticity of soliton collisions for the 5D energy critical wave equation. Zbl 1408.76111
Martel, Yvan; 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
21
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
18
2017
Stability of ODE blow-up for the energy critical semilinear heat equation. Zbl 1364.35156
Collot, Charles; Merle, Frank; Raphaël, Pierre
5
2017
Solutions of the focusing nonradial critical wave equation with the compactness property. Zbl 1348.35141
Duyckaerts, Thomas; Kenig, Carlos; Merle, Frank
15
2016
Codimension one threshold manifold for the critical gKdV equation. Zbl 1336.35315
Martel, Yvan; Merle, Frank; Nakanishi, Kenji; Raphaël, Pierre
13
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
13
2016
Construction of multi-solitons for the energy-critical wave equation in dimension 5. Zbl 1359.35166
Martel, Yvan; Merle, Frank
11
2016
Concentration-compactness and universal profiles for the non-radial energy critical wave equation. Zbl 1339.35186
Duyckaerts, Thomas; Kenig, Carlos; Merle, Frank
9
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
26
2015
Blow up for the critical gKdV equation. II: Minimal mass dynamics. Zbl 1326.35320
Martel, Yvan; Merle, Frank; Raphaël, Pierre
22
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
22
2015
Type II blow up for the energy supercritical NLS. Zbl 1347.35215
Merle, Frank; Raphaël, Pierre; Rodnianski, Igor
16
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
10
2015
On the nonexistence of pure multi-solitons for the quartic gKdV equation. Zbl 1315.35191
Martel, Yvan; Merle, Frank
3
2015
Scattering for radial, bounded solutions of focusing supercritical wave equations. Zbl 1310.35171
Duyckaerts, Thomas; Kenig, Carlos; Merle, Frank
27
2014
Blow up for the critical generalized Korteweg-de Vries equation. I: Dynamics near the soliton. Zbl 1301.35137
Martel, Yvan; Merle, Frank; Raphaël, Pierre
27
2014
On collapsing ring blow-up solutions to the mass supercritical nonlinear Schrödinger equation. Zbl 1292.35283
Merle, Frank; Raphaël, Pierre; Szeftel, Jeremie
9
2014
Near soliton dynamics and singularity formation for \( L^2\) critical problems. Zbl 1304.35650
Martel, Y.; Merle, F.; Raphaël, P.; Szeftel, J.
3
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
60
2013
Blowup dynamics for smooth data equivariant solutions to the critical Schrödinger map problem. Zbl 1326.35052
Merle, Frank; Raphaël, Pierre; Rodnianski, Igor
37
2013
The instability of Bourgain-Wang solutions for the \(L^2\) critical NLS. Zbl 1294.35145
Merle, Frank; Raphaël, Pierre; Szeftel, Jeremie
13
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
Profiles of bounded radial solutions of the focusing, energy-critical wave equation. Zbl 1258.35148
Duyckaerts, Thomas; Kenig, Carlos; Merle, Frank
43
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
43
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
32
2012
Isolatedness of characteristic points at blowup for a 1-dimensional semilinear wave equation. Zbl 1270.35320
Merle, Frank; Zaag, Hatem
20
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
58
2011
Nondispersive radial solutions to energy supercritical non-linear wave equations, with applications. Zbl 1241.35136
Kenig, Carlos E.; Merle, Frank
39
2011
Construction of multi-soliton solutions for the \(L^2\)-supercritical gKdV and NLS equations. Zbl 1273.35234
Côte, Raphaël; Martel, Yvan; Merle, Frank
33
2011
Description of two soliton collision for the quartic gKdV equation. Zbl 1300.37045
Martel, Yvan; Merle, Frank
28
2011
Threshold and generic type I behaviors for a supercritical nonlinear heat equation. Zbl 1223.35088
Matano, Hiroshi; Merle, Frank
24
2011
Inelastic interaction of nearly equal solitons for the quartic gKdV equation. Zbl 1230.35121
Martel, Yvan; Merle, Frank
18
2011
Blow up dynamics for smooth equivariant solutions to the energy critical Schrödinger map. Zbl 1213.35139
Merle, Frank; Raphaël, Pierre; Rodnianski, Igor
16
2011
Radial solutions to energy supercritical wave equations in odd dimensions. Zbl 1298.35119
Kenig, Carlos E.; Merle, Frank
15
2011
Blow-up behavior outside the origin for a semilinear wave equation in the radial case. Zbl 1222.35126
Merle, Frank; Zaag, Hatem
14
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
45
2010
Stable self-similar blow-up dynamics for slightly \(L^{2}\) super-critical NLS equations. Zbl 1204.35153
Merle, Frank; Raphaël, Pierre; Szeftel, Jeremie
17
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
50
2009
Dynamic of threshold solutions for energy-critical NLS. Zbl 1232.35150
Duyckaerts, Thomas; Merle, Frank
47
2009
Stability of two soliton collision for nonintegrable gKdV equations. Zbl 1179.35291
Martel, Yvan; Merle, Frank
21
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
172
2008
Dynamics of threshold solutions for energy-critical wave equation. Zbl 1159.35043
Duyckaerts, Thomas; Merle, Frank
46
2008
Asymptotic stability of solitons of the gKdV equations with general nonlinearity. Zbl 1153.35068
Martel, Yvan; Merle, Frank
31
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
30
2008
Blow up of the critical norm for some radial \(L^2\) super critical nonlinear Schrödinger equations. Zbl 1188.35182
Merle, Frank; Raphaël, Pierre
19
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
15
2008
Refined asymptotics around solitons for gKdV equations. Zbl 1137.35062
Martel, Yvan; Merle, Frank
11
2008
Note on coupled linear systems related to two soliton collision for the quartic gKdV equation. Zbl 1188.35164
Martel, Yvan; Merle, Frank
3
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
35
2007
On the energy critical focusing non-linear wave equation. Zbl 1173.35601
Merle, Frank
1
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
260
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
68
2006
Multi solitary waves for nonlinear Schrödinger equations. Zbl 1133.35093
Martel, Yvan; Merle, Frank
41
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
40
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
25
2006
Asymptotic stability and Liouville theorem for scalar viscous conservation laws in cylinders. Zbl 1105.35051
Kenig, Carlos E.; Merle, Frank
3
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
109
2005
Profiles and quantization of the blow up mass for critical nonlinear Schrödinger equation. Zbl 1062.35137
Merle, Frank; Raphaël, Pierre
68
2005
Asymptotic stability of solitons of the subcritical gKdV equations revisited. Zbl 1064.35171
Martel, Yvan; Merle, Frank
50
2005
Determination of the blow-up rate for a critical semilinear wave equation. Zbl 1136.35055
Merle, Frank; Zaag, Hatem
37
2005
On growth rate near the blowup surface for semilinear wave equations. Zbl 1160.35478
Merle, Frank; Zaag, Hatem
22
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
95
2004
On nonexistence of type II blowup for a supercritical nonlinear heat equation. Zbl 1112.35098
Matano, Hiroshi; Merle, Frank
72
2004
Review on blow up and asymptotic dynamics for critical and subcritical gKdV equations. Zbl 1071.35114
Martel, Yvan; Merle, Frank
3
2004
Sharp upper bound on the blow-up rate for the critical nonlinear Schrödinger equation. Zbl 1061.35135
Merle, Frank; Raphaël, Pierre
67
2003
Determination of the blow-up rate for the semilinear wave equation. Zbl 1052.35043
Merle, Frank; Zaag, Hatem
38
2003
\(L^2\) stability of solitons for KdV equation. Zbl 1022.35061
Merle, F.; Vega, L.
25
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
68
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
56
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
47
2002
Nonexistence of blow-up solution with minimal \(L^2\)-mass for the critical gKdV equation. Zbl 1033.35102
Martel, Yvan; Merle, Frank
18
2002
O. D. E. type behavior of blow-up solutions of nonlinear heat equations. Zbl 1009.35039
Merle, Frank; Zaag, Hatem
8
2002
Asymptotic stability of solitons for subcritical generalized KdV equations. Zbl 0981.35073
Martel, Yvan; Merle, Frank
63
2001
Existence of blow-up solutions in the energy space for the critical generalized KdV equation. Zbl 0970.35128
Merle, Frank
54
2001
Instability of solitons for the critical generalized Korteweg-de Vries equation. Zbl 0985.35071
Martel, Y.; Merle, F.
47
2001
Optimal bounds on positive blow-up solutions for a semilinear wave equation. Zbl 0989.35090
Antonini, Christophe; Merle, Frank
20
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
2
2001
A Liouville theorem for the critical generalized Korteweg-de Vries equation. Zbl 0963.37058
Martel, Yvan; Merle, Frank
56
2000
A Liouville theorem for vector-valued nonlinear heat equations and applications. Zbl 0939.35086
Merle, Frank; Zaag, Hatem
43
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.
27
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.
78
1998
Optimal estimates for blowup rate and behavior for nonlinear heat equations. Zbl 0899.35044
Merle, Frank; Zaag, Hatem
54
1998
Refined uniform estimates at blow-up and applications for nonlinear heat equations. Zbl 0926.35024
Merle, F.; Zaag, H.
25
1998
Blow-up phenomena for critical nonlinear Schrödinger and Zakharov equations. Zbl 0896.35123
Merle, Frank
5
1998
...and 31 more Documents
all top 5

Cited by 1,302 Authors

67 Merle, Frank
38 Wei, Juncheng
37 Martel, Yvan
36 Raphael, Pierre
36 Zaag, Hatem
31 Bartolucci, Daniele
31 Kenig, Carlos Eduardo
28 Lin, Chang-Shou
23 Muñoz, Claudio
21 Krieger, Joachim
21 Musso, Monica
18 Schlag, Wilhelm
18 Zhang, Jian
17 Del Pino, Manuel A.
17 Donninger, Roland
17 Miao, Changxing
17 Souplet, Philippe
16 Mizoguchi, Noriko
16 Nakanishi, Kenji
16 Tarantello, Gabriella
16 Zhu, Shihui
15 Ding, Yanheng
15 Duyckaerts, Thomas
15 Zhao, Lifeng
14 Guo, Boling
14 Martinazzi, Luca
14 Zheng, Jiqiang
14 Zhou, Chunqin
13 Côte, Raphaël
13 Malchiodi, Andrea
13 Saanouni, Tarek
13 Suzuki, Takashi
13 Visan, Monica
13 Yang, Wen
12 Holmer, Justin
12 Roudenko, Svetlana
12 Tataru, Daniel
12 Xu, Guixiang
11 Farah, Luiz Gustavo
11 Jevnikar, Aleks
11 Lawrie, Andrew G. W.
11 Wang, Guofang
11 Zhang, Xiaoyi
10 Bahouri, Hajer
10 Cazenave, Thierry
10 Jost, Jürgen
10 Killip, Rowan
10 Lee, Youngae
10 Nguyen, Van Tien
9 Fibich, Gadi
9 Ghoul, Tej-Eddine
9 Ibrahim, Slim
9 Miyamoto, Yasuhito
8 Carles, Rémi
8 Colliander, James E.
8 Cuccagna, Scipio
8 Dodson, Benjamin G.
8 Fang, Daoyuan
8 Galaktionov, Victor Aleksandrovich
8 Gan, Zaihui
8 Grossi, Massimo
8 Lenzmann, Enno
8 Li, Dong
8 Li, Xiaoguang
8 Masmoudi, Nader
8 Pausader, Benoît
8 Pistoia, Angela
8 Struwe, Michael
8 Tao, Terence
8 Tzvetkov, Nikolay
8 Zhang, Lei
7 Choe, Kwangseok
7 Gao, Yanfang
7 Hamza, Mohamed Ali
7 Ishige, Kazuhiro
7 Klein, Christian
7 Lei, Yutian
7 Liu, Yue
7 Mizumachi, Tetsu
7 Murphy, Jason
7 Perelman, Galina
7 Ponce, Gustavo
7 Saut, Jean-Claude
6 Banica, Valeria
6 Battaglia, Luca
6 Chanillo, Sagun
6 Cheng, Xing
6 Collot, Charles
6 de Marchis, Francesca
6 Deng, Shengbing
6 Dinh, Van Duong
6 Dolbeault, Jean
6 Fujishima, Yohei
6 Guo, Jong-Shenq
6 Guo, Zihua
6 Jendrej, Jacek
6 Liu, Xiaoying
6 Lucia, Marcello
6 Maeda, Masaya
6 Masaki, Satoshi
...and 1,202 more Authors
all top 5

Cited in 219 Serials

144 Journal of Differential Equations
81 Journal of Functional Analysis
68 Communications in Mathematical Physics
68 Journal of Mathematical Analysis and Applications
67 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods
67 Calculus of Variations and Partial Differential Equations
61 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire
51 Communications in Partial Differential Equations
46 Transactions of the American Mathematical Society
43 Discrete and Continuous Dynamical Systems
42 Journal of Mathematical Physics
31 Archive for Rational Mechanics and Analysis
30 Mathematische Annalen
26 Communications on Pure and Applied Analysis
24 Journal de Mathématiques Pures et Appliquées. Neuvième Série
24 Communications in Contemporary Mathematics
23 Physica D
22 Duke Mathematical Journal
21 Proceedings of the American Mathematical Society
19 Advances in Mathematics
19 Acta Mathematica Sinica. English Series
17 Communications on Pure and Applied Mathematics
17 Comptes Rendus. Mathématique. Académie des Sciences, Paris
16 Inventiones Mathematicae
15 Journal of Hyperbolic Differential Equations
14 Séminaire Laurent Schwartz. EDP et Applications
13 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics
13 SIAM Journal on Mathematical Analysis
13 NoDEA. Nonlinear Differential Equations and Applications
12 Science China. Mathematics
11 Journal d’Analyse Mathématique
11 Journal of the American Mathematical Society
11 Journal of Dynamics and Differential Equations
11 Journal of the European Mathematical Society (JEMS)
11 Analysis & PDE
10 Nonlinearity
10 Journal of Evolution Equations
9 Applicable Analysis
9 ZAMP. Zeitschrift für angewandte Mathematik und Physik
9 Annali di Matematica Pura ed Applicata. Serie Quarta
9 Nonlinear Analysis. Real World Applications
9 Nonlinear Analysis. Theory, Methods & Applications
9 Annals of PDE
8 Mathematical Methods in the Applied Sciences
8 Applied Mathematics and Computation
8 Advanced Nonlinear Studies
7 Applied Mathematics Letters
7 Geometric and Functional Analysis. GAFA
6 Mathematische Zeitschrift
6 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences
6 Bulletin des Sciences Mathématiques
6 Annales Henri Poincaré
5 Journal of Computational Physics
5 Manuscripta Mathematica
5 Chinese Annals of Mathematics. Series B
5 Revista Matemática Iberoamericana
5 Bulletin of the American Mathematical Society. New Series
5 Journal of Nonlinear Science
5 Discrete and Continuous Dynamical Systems. Series B
5 Milan Journal of Mathematics
4 Computers & Mathematics with Applications
4 Reviews in Mathematical Physics
4 Journal of Computational and Applied Mathematics
4 Memoirs of the American Mathematical Society
4 The Journal of Geometric Analysis
4 Journal of Elliptic and Parabolic Equations
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 Indiana University Mathematics Journal
3 Proceedings of the London Mathematical Society. Third Series
3 Asymptotic Analysis
3 Annales de l’Institut Henri Poincaré. Physique Théorique
3 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations
3 Annals of Mathematics. Second Series
3 Communications in Nonlinear Science and Numerical Simulation
3 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V
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 Kyoto Journal of Mathematics
3 Communications in Mathematics and Statistics
2 Journal of Statistical Physics
2 Letters in Mathematical Physics
2 Rocky Mountain Journal of Mathematics
2 Wave Motion
2 Annales de l’Institut Fourier
2 Bulletin de la Société Mathématique de France
2 Czechoslovak Mathematical Journal
2 Publications Mathématiques
2 Journal für die Reine und Angewandte Mathematik
2 Monatshefte für Mathematik
2 Numerische Mathematik
2 Proceedings of the Edinburgh Mathematical Society. Series II
2 Publications of the Research Institute for Mathematical Sciences, Kyoto University
2 Rendiconti del Seminario Matematico della Università di Padova
2 SIAM Journal on Numerical Analysis
2 Studies in Applied Mathematics
2 Acta Mathematicae Applicatae Sinica. English Series
...and 119 more Serials
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Cited in 46 Fields

1,526 Partial differential equations (35-XX)
109 Dynamical systems and ergodic theory (37-XX)
107 Global analysis, analysis on manifolds (58-XX)
104 Quantum theory (81-XX)
95 Fluid mechanics (76-XX)
73 Differential geometry (53-XX)
54 Numerical analysis (65-XX)
47 Statistical mechanics, structure of matter (82-XX)
46 Operator theory (47-XX)
38 Functional analysis (46-XX)
36 Calculus of variations and optimal control; optimization (49-XX)
28 Ordinary differential equations (34-XX)
28 Optics, electromagnetic theory (78-XX)
20 Harmonic analysis on Euclidean spaces (42-XX)
19 Biology and other natural sciences (92-XX)
17 Mechanics of deformable solids (74-XX)
14 Real functions (26-XX)
11 Functions of a complex variable (30-XX)
10 Mechanics of particles and systems (70-XX)
10 Relativity and gravitational theory (83-XX)
9 Probability theory and stochastic processes (60-XX)
8 Systems theory; control (93-XX)
6 Astronomy and astrophysics (85-XX)
5 Potential theory (31-XX)
5 Integral equations (45-XX)
4 Special functions (33-XX)
4 Difference and functional equations (39-XX)
4 Classical thermodynamics, heat transfer (80-XX)
3 Linear and multilinear algebra; matrix theory (15-XX)
3 Statistics (62-XX)
2 Nonassociative rings and algebras (17-XX)
2 Several complex variables and analytic spaces (32-XX)
2 Geophysics (86-XX)
1 General and overarching topics; collections (00-XX)
1 History and biography (01-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 Measure and integration (28-XX)
1 Approximations and expansions (41-XX)
1 Abstract harmonic analysis (43-XX)
1 Geometry (51-XX)
1 Manifolds and cell complexes (57-XX)
1 Computer science (68-XX)
1 Operations research, mathematical programming (90-XX)

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