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Author ID: gerard.patrick Recent zbMATH articles by "Gerard, Patrick"
Published as: Gérard, Patrick; Gérard, P.; Gerard, Patrick; Gerard, P.
Homepage: https://www.imo.universite-paris-saclay.fr/~patrick.gerard/
External Links: MGP · Wikidata · dblp · GND · IdRef · theses.fr
Member of Collective: Bourbaki, Nicolas
all top 5

Serials

12 Séminaire Équations aux Dérivées Partielles
4 Séminaire Laurent Schwartz. EDP et Applications
3 Communications on Pure and Applied Mathematics
3 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série
3 Inventiones Mathematicae
3 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire
2 Archive for Rational Mechanics and Analysis
2 American Journal of Mathematics
2 Bulletin de la Société Mathématique de France
2 Duke Mathematical Journal
2 Journal of Functional Analysis
2 Communications in Partial Differential Equations
2 Journal de Mathématiques Pures et Appliquées. Neuvième Série
2 SIAM Journal on Mathematical Analysis
2 Mathematical Research Letters
2 Comptes Rendus de l’Académie des Sciences. Série I. Mathématique
2 Comptes Rendus. Mathématique. Académie des Sciences, Paris
2 Tunisian Journal of Mathematics
1 Journal d’Analyse Mathématique
1 Letters in Mathematical Physics
1 Mathematical Methods in the Applied Sciences
1 Nonlinearity
1 Studia Mathematica
1 Acta Mathematica
1 Annales de l’Institut Fourier
1 Gazette des Mathématiciens
1 Journal of the London Mathematical Society. Second Series
1 Mathematische Zeitschrift
1 Mathematika
1 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods
1 Quarterly of Applied Mathematics
1 Transactions of the American Mathematical Society
1 Journal of the American Mathematical Society
1 IMRN. International Mathematics Research Notices
1 Geometric and Functional Analysis. GAFA
1 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations
1 Annales Henri Poincaré
1 Journal of Nonlinear Mathematical Physics
1 Journal of the Institute of Mathematics of Jussieu
1 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V
1 Journal of Hyperbolic Differential Equations
1 Astérisque
1 Graduate Studies in Mathematics
1 Kinetic and Related Models
1 Analysis & PDE
1 Science China. Mathematics
1 Journal of Spectral Theory
1 Annals of PDE
1 Pure and Applied Analysis
1 Savoirs Actuels

Publications by Year

Citations contained in zbMATH Open

90 Publications have been cited 2,482 times in 1,658 Documents Cited by Year
Homogenization limits and Wigner transforms. Zbl 0881.35099
Gérard, Patrick; Markowich, Peter A.; Mauser, Norbert J.; Poupaud, Frédéric
209
1997
High frequency approximation of solutions to critical nonlinear wave equations. Zbl 0919.35089
Bahouri, Hajer; Gérard, Patrick
208
1999
Microlocal defect measures. Zbl 0770.35001
Gérard, Patrick
205
1991
Strichartz inequalities and the nonlinear Schrödinger equation on compact manifolds. Zbl 1067.58027
Burq, N.; Gérard, P.; Tzvetkov, N.
198
2004
A necessary and sufficient condition for the exact controllability of the wave equation. (Condition nécessaire et suffisante pour la contrôlabilité exacte des ondes.) Zbl 0906.93008
Burq, Nicolas; Gérard, Patrick
100
1997
Ergodic properties of eigenfunctions for the Dirichlet problem. Zbl 0788.35103
Gérard, Patrick; Leichtnam, Eric
99
1993
Pseudo-differential operators and the Nash-Moser theorem. (Opérateurs pseudo-différentiels et théorème de Nash-Moser.) Zbl 0791.47044
Alinhac, Serge; Gérard, Patrick
87
1991
Pseudo-differential operators and the Nash–Moser theorem. Transl. from the French by Stephen S. Wilson. Zbl 1121.47033
Alinhac, Serge; Gérard, Patrick
77
2007
Bilinear eigenfunction estimates and the nonlinear Schrödinger equation on surfaces. Zbl 1092.35099
Burq, N.; Gérard, P.; Tzvetkov, N.
75
2005
Restrictions of the Laplace-Beltrami eigenfunctions to submanifolds. Zbl 1131.35053
Burq, N.; Gérard, P.; Tzvetkov, N.
73
2007
Description of the lack of compactness for the Sobolev imbedding. Zbl 0907.46027
Gérard, P.
70
1998
The cubic Szegő equation. (L’équation de Szegő cubique.) Zbl 1228.35225
Gérard, Patrick; Grellier, Sandrine
58
2010
An instability property of the nonlinear Schrödinger equation on \(S^d\). Zbl 1003.35113
Burq, N.; Gérard, P.; Tzvetkov, N.
58
2002
Stabilization and control for the nonlinear Schrödinger equation on a compact surface. Zbl 1127.93015
Dehman, B.; Gérard, P.; Lebeau, G.
58
2006
Multilinear eigenfunction estimates and global existence for the three dimensional nonlinear Schrödinger equations. Zbl 1116.35109
Burq, Nicolas; Gérard, Patrick; Tzvetkov, Nikolay
54
2005
The Cauchy problem for the Gross–Pitaevskii equation. Zbl 1122.35133
Gérard, P.
48
2006
On nonlinear Schrödinger equations in exterior domains. Zbl 1061.35126
Burq, N.; Gérard, P.; Tzvetkov, N.
44
2004
Besov spaces and Strichartz estimates on the Heisenberg group. (Espaces de Besov et estimations de Strichartz généralisées sur le groupe de Heisenberg.) Zbl 0965.22010
Bahouri, Hajer; Gérard, Patrick; Xu, Chao-Jiang
44
2000
Effective integrable dynamics for a certain nonlinear wave equation. Zbl 1268.35013
Gérard, Patrick; Grellier, Sandrine
44
2012
Oscillations of concentration effects in semilinear dispersive wave equations. Zbl 0868.35075
Gérard, Patrick
42
1996
Sharp Sobolev inequalities. (Inégalités de Sobolev précisées.) Zbl 1066.46501
Gerard, Patrick; Meyer, Yves; Oru, Frédérique
41
1997
Semi-classical measures and eigenvalue crossings. (Mesures semi-classiques et croisement de modes.) Zbl 0996.35004
Fermanian-Kammerer, Clotilde; Gérard, Patrick
39
2002
The cubic Szegő equation and Hankel operators. Zbl 1410.37001
Gérard, Patrick; Grellier, Sandrine
32
2017
Mesures semi-classiques et ondes de Bloch. (Semiclassical measures and Bloch waves). Zbl 0739.35096
Gérard, P.
30
1991
A Landau-Zener formula for non-degenerated involutive codimension 3 crossings. Zbl 1049.81029
Fermanian Kammerer, Clotilde; Gérard, Patrick
28
2003
Invariant tori for the cubic Szegö equation. Zbl 1252.35026
Gérard, Patrick; Grellier, Sandrine
27
2012
Two singular dynamics of the nonlinear Schrödinger equation on a plane domain. Zbl 1044.35084
Burq, N.; Gérard, P.; Tzvetkov, N.
25
2003
The Gross-Pitaevskii equation in the energy space. Zbl 1166.35373
Gérard, Patrick
22
2008
A two-soliton with transient turbulent regime for the cubic half-wave equation on the real line. Zbl 1397.35062
Gérard, Patrick; Lenzmann, Enno; Pocovnicu, Oana; Raphaël, Pierre
21
2018
Orbital stability of traveling waves for the one-dimensional Gross-Pitaevskii equation. Zbl 1232.35152
Gérard, Patrick; Zhang, Zhifei
21
2009
An explicit formula for the cubic Szegő equation. Zbl 1318.37024
Gérard, Patrick; Grellier, Sandrine
20
2015
On the spectrum of the Lax operator of the Benjamin-Ono equation on the torus. Zbl 1452.37070
Gérard, Patrick; Kappeler, Thomas; Topalov, Petar
17
2020
Moyennisation et régularité deux-microlocale. (Second microlocal averaging and regularity). Zbl 0725.35003
Gérard, Patrick
16
1990
On the integrability of the Benjamin-Ono equation on the torus. Zbl 1471.35354
Gérard, Patrick; Kappeler, Thomas
16
2021
On the cubic lowest Landau level equation. Zbl 1412.82034
Gérard, Patrick; Germain, Pierre; Thomann, Laurent
16
2019
Averaging regularity results for PDEs under transversality assumptions. Zbl 0832.35020
Gérard, Patrick; Golse, François
16
1992
Diffraction of a wave at a corner. (Diffusion d’une onde par un coin.) Zbl 0779.35063
Gérard, Patrick; Lebeau, Gilles
14
1993
On the radius of analyticity of solutions to the cubic Szegő equation. Zbl 1332.35058
Gérard, Patrick; Guo, Yanqiu; Titi, Edriss S.
14
2015
Profile decomposition for the wave equation outside a convex obstacle. Zbl 0980.35088
Gallagher, Isabelle; Gérard, Patrick
14
2001
Global solutions for the nonlinear Schrödinger equation on three-dimensional compact manifolds. Zbl 1180.35475
Burq, N.; Gérard, P.; Tzvetkov, N.
14
2007
The Cauchy problem for the nonlinear Schrödinger equation on a compact manifold. Zbl 1362.35282
Burq, Nicolas; Gérard, Patrick; Tzvetkov, Nikolay
10
2003
Nonlinear Schrödinger equations in inhomogeneous media: wellposedness and illposedness of the Cauchy problem. Zbl 1106.35096
Gérard, Patrick
9
2006
Recent results concerning two-dimensional incompressible perfect fluids (after J.-Y. Chemin and J.-M. Delort). (Résultats récents sur les fluides parfaits incompressibles bidimensionnels (d’après J.-Y. Chemin et J.-M. Delort).) Zbl 1154.76321
Gérard, Patrick
9
1992
A Lax pair structure for the half-wave maps equation. Zbl 1393.37074
Gérard, Patrick; Lenzmann, Enno
9
2018
Stabilization of wave equations on the torus with rough dampings. Zbl 1462.35070
Burq, Nicolas; Gérard, Patrick
9
2020
Propagation de la régularité locale de solutions d’équations hyperboliques non linéaires. (Propagation of local smoothness for solutions of nonlinear hyperbolic equations). Zbl 0617.35079
Gerard, P.; Rauch, J.
8
1987
Wigner measure propagation and conical singularity for general initial data. Zbl 1288.35408
Fermanian-Kammerer, Clotilde; Gérard, Patrick; Lasser, Caroline
8
2013
Multilinear estimates for the Laplace spectral projectors on compact manifolds. Zbl 1040.58011
Burq, Nicolas; Gérard, Patrick; Tzvetkov, Nikolay
8
2004
Remarks on the semiclassical analysis of the nonlinear Schrödinger equation. (Remarques sur l’analyse semi-classique de l’équation de Schrödinger non linéaire.) Zbl 0874.35111
Gérard, Patrick
7
1993
An inverse problem for self-adjoint positive Hankel operators. Zbl 1338.47024
Gérard, Patrick; Pushnitski, Alexander
7
2015
Nonlinear Schrödinger equation on four-dimensional compact manifolds. Zbl 1183.35251
Gérard, Patrick; Pierfelice, Vittoria
7
2010
A drift homogenization problem revisited. Zbl 1270.35058
Briane, Marc; Gérard, Patrick
5
2012
The Cauchy problem for the nonlinear Schrödinger equation on compact manifolds. Zbl 1084.35086
Burq, N.; Gérard, P.; Tzvetkov, N.
5
2004
Inverse spectral problems for compact Hankel operators. Zbl 1304.47038
Gérard, Patrick; Grellier, Sandrine
5
2014
Sensitivity phenomena for certain thin elastic shells with edges. Zbl 0989.74047
Gerard, Patrick; Sanchez-Palencia, Evariste
5
2000
The Schrödinger equation on a compact manifold: Strichartz estimates and applications. Zbl 1043.58019
Burq, Nicolas; Gérard, Patrick; Tzvetkov, Nikolay
5
2001
Nonlinear Schrödinger equations on compact manifolds. Zbl 1076.35115
Gérard, P.
4
2005
On the Benjamin-Ono equation on \(\mathbb{T}\) and its periodic and quasiperiodic solutions. Zbl 1495.37060
Gérard, Patrick; Kappeler, Thomas; Topalov, Petar
4
2022
Weighted model spaces and Schmidt subspaces of Hankel operators. Zbl 1448.47040
Gérard, Patrick; Pushnitski, Alexander
4
2020
On the analytic Birkhoff normal form of the Benjamin-Ono equation and applications. Zbl 1521.37085
Gérard, Patrick; Kappeler, Thomas; Topalov, Petar
4
2022
Concentration effects in critical nonlinear wave equation and scattering theory. Zbl 0926.35090
Bahouri, Hajer; Gérard, Patrick
3
1997
On the growth of Sobolev norms for the cubic Szegő equation. Zbl 1355.35022
Gérard, Patrick; Grellier, Sandrine
3
2016
Inverse spectral theory for a class of non-compact Hankel operators. Zbl 07036937
Gérard, Patrick; Pushnitski, Alexander
3
2019
The Schrödinger-Poisson system on the sphere. Zbl 1231.35229
Gérard, Patrick; Méhats, Florian
3
2011
Solutions conormales analytiques d’équations hyperboliques non linéaires. (Conormal analytic solutions of nonlinear hyperbolic equations). Zbl 0639.35054
Gerard, Patrick
3
1988
Moyennes de solutions d’équations aux dérivées partielles. (Means of solutions of partial differential equations). Zbl 0657.35020
Gerard, P.
3
1987
Semiclassical measures and crossing of modes. (Mesures semi-classiques et croisement de modes.) Zbl 1055.81534
Fermanian Kammerer, Clotilde; Gerard, Patrick
3
2000
The cubic Szegö equation. (L’equation de Szegö cubique.) Zbl 1213.35397
Gérard, Patrick; Grellier, Sandrine
3
2010
The cubic Szegő flow at low regularity. Zbl 1475.35434
Gérard, Patrick; Koch, Herbert
3
2017
A microlocal version of concentration-compactness. Zbl 0868.35005
Gérard, Patrick
2
1996
A compactness result for generalized Radon transforms. Zbl 0864.44001
Gérard, Patrick; Golse, François; Wennberg, Bernt
2
1996
Compacité par compensation et régularité 2-microlocale. (Compensated compactness and 2-microlocal regularity). Zbl 0707.35032
Gérard, P.
2
1989
On a damped Szegö equation (with an appendix in collaboration with Christian Klein). Zbl 1448.35022
Gérard, Patrick; Grellier, Sandrine
2
2020
Wave turbulence and complete integrability. Zbl 1442.35419
Gérard, Patrick
2
2019
A Landau-Zener formula for a generic crossing in codimension 2. (Une formule de Landau-Zener pour un croisement générique de codimension 2.) Zbl 1292.35252
Fermanian Kammerer, Clotilde; Gérard, Patrick
2
2002
A mean-field toy model for resonant transport. Zbl 1194.35462
Gerard, Patrick; Pallard, Christophe
2
2010
A nonlinear Fourier transform for the Benjamin-Ono equation on the torus and applications. Zbl 1479.35020
Gérard, Patrick
2
2020
Solutions globales du problème de Cauchy pour l’équation de Boltzmann [d’après R. J. Di Perna et P. L. Lions]. Zbl 0704.76041
Gérard, Patrick
1
1988
Regularization by averaging for solutions of partial differential equations. Zbl 0724.35115
Gérard, P.
1
1988
Two-scale Wigner measures and the Landau-Zener formulas. Zbl 1322.81059
Kammerer, C. Fermanian; Gérard, P.
1
2004
An introduction to the cubic Szegö equation. Zbl 1348.35232
Gérard, Patrick
1
2013
Inverse spectral problem for a pair of self-adjoint Hankel operators. Zbl 1449.35032
Gérard, Patrick; Grellier, Sandrine
1
2017
A survey of the Szegő equation. Zbl 1428.35067
Gérard, Patrick; Grellier, Sandrine
1
2019
Generic colourful tori and inverse spectral transform for Hankel operators. Zbl 1409.35045
Gérard, Patrick; Grellier, Sandrine
1
2019
The structure of Schmidt subspaces of Hankel operators: a short proof. Zbl 1514.47053
Gérard, Patrick; Pushnitski, Alexander
1
2021
Régularité de moyennes de solutions d’équations aux dérivées partielles. (Regularity of means of solutions of partial differential equations). Zbl 0639.35010
Gerard, Patrick
1
1987
An example of singular dynamics for the nonlinear Schrödinger equation on bounded domains. Zbl 1210.35225
Burg, N.; Gérard, P.; Tzvetkov, N.
1
2003
Generalized geometric optics for critical nonlinear waves. (Optique géométrique généralisée pour les ondes non linéaires critiques.) Zbl 1068.35522
Bahouri, Hajer; Gerard, Patrick
1
1997
A Landau-Zener formula for two-scaled Wigner measures. Zbl 1145.81368
Fermanian Kammerer, Clotilde; Gerard, Patrick
1
2004
Unbounded Hankel operators and the flow of the cubic Szegő equation. Zbl 1525.47058
Gérard, Patrick; Pushnitski, Alexander
1
2023
Unbounded Hankel operators and the flow of the cubic Szegő equation. Zbl 1525.47058
Gérard, Patrick; Pushnitski, Alexander
1
2023
On the Benjamin-Ono equation on \(\mathbb{T}\) and its periodic and quasiperiodic solutions. Zbl 1495.37060
Gérard, Patrick; Kappeler, Thomas; Topalov, Petar
4
2022
On the analytic Birkhoff normal form of the Benjamin-Ono equation and applications. Zbl 1521.37085
Gérard, Patrick; Kappeler, Thomas; Topalov, Petar
4
2022
On the integrability of the Benjamin-Ono equation on the torus. Zbl 1471.35354
Gérard, Patrick; Kappeler, Thomas
16
2021
The structure of Schmidt subspaces of Hankel operators: a short proof. Zbl 1514.47053
Gérard, Patrick; Pushnitski, Alexander
1
2021
On the spectrum of the Lax operator of the Benjamin-Ono equation on the torus. Zbl 1452.37070
Gérard, Patrick; Kappeler, Thomas; Topalov, Petar
17
2020
Stabilization of wave equations on the torus with rough dampings. Zbl 1462.35070
Burq, Nicolas; Gérard, Patrick
9
2020
Weighted model spaces and Schmidt subspaces of Hankel operators. Zbl 1448.47040
Gérard, Patrick; Pushnitski, Alexander
4
2020
On a damped Szegö equation (with an appendix in collaboration with Christian Klein). Zbl 1448.35022
Gérard, Patrick; Grellier, Sandrine
2
2020
A nonlinear Fourier transform for the Benjamin-Ono equation on the torus and applications. Zbl 1479.35020
Gérard, Patrick
2
2020
On the cubic lowest Landau level equation. Zbl 1412.82034
Gérard, Patrick; Germain, Pierre; Thomann, Laurent
16
2019
Inverse spectral theory for a class of non-compact Hankel operators. Zbl 07036937
Gérard, Patrick; Pushnitski, Alexander
3
2019
Wave turbulence and complete integrability. Zbl 1442.35419
Gérard, Patrick
2
2019
A survey of the Szegő equation. Zbl 1428.35067
Gérard, Patrick; Grellier, Sandrine
1
2019
Generic colourful tori and inverse spectral transform for Hankel operators. Zbl 1409.35045
Gérard, Patrick; Grellier, Sandrine
1
2019
A two-soliton with transient turbulent regime for the cubic half-wave equation on the real line. Zbl 1397.35062
Gérard, Patrick; Lenzmann, Enno; Pocovnicu, Oana; Raphaël, Pierre
21
2018
A Lax pair structure for the half-wave maps equation. Zbl 1393.37074
Gérard, Patrick; Lenzmann, Enno
9
2018
The cubic Szegő equation and Hankel operators. Zbl 1410.37001
Gérard, Patrick; Grellier, Sandrine
32
2017
The cubic Szegő flow at low regularity. Zbl 1475.35434
Gérard, Patrick; Koch, Herbert
3
2017
Inverse spectral problem for a pair of self-adjoint Hankel operators. Zbl 1449.35032
Gérard, Patrick; Grellier, Sandrine
1
2017
On the growth of Sobolev norms for the cubic Szegő equation. Zbl 1355.35022
Gérard, Patrick; Grellier, Sandrine
3
2016
An explicit formula for the cubic Szegő equation. Zbl 1318.37024
Gérard, Patrick; Grellier, Sandrine
20
2015
On the radius of analyticity of solutions to the cubic Szegő equation. Zbl 1332.35058
Gérard, Patrick; Guo, Yanqiu; Titi, Edriss S.
14
2015
An inverse problem for self-adjoint positive Hankel operators. Zbl 1338.47024
Gérard, Patrick; Pushnitski, Alexander
7
2015
Inverse spectral problems for compact Hankel operators. Zbl 1304.47038
Gérard, Patrick; Grellier, Sandrine
5
2014
Wigner measure propagation and conical singularity for general initial data. Zbl 1288.35408
Fermanian-Kammerer, Clotilde; Gérard, Patrick; Lasser, Caroline
8
2013
An introduction to the cubic Szegö equation. Zbl 1348.35232
Gérard, Patrick
1
2013
Effective integrable dynamics for a certain nonlinear wave equation. Zbl 1268.35013
Gérard, Patrick; Grellier, Sandrine
44
2012
Invariant tori for the cubic Szegö equation. Zbl 1252.35026
Gérard, Patrick; Grellier, Sandrine
27
2012
A drift homogenization problem revisited. Zbl 1270.35058
Briane, Marc; Gérard, Patrick
5
2012
The Schrödinger-Poisson system on the sphere. Zbl 1231.35229
Gérard, Patrick; Méhats, Florian
3
2011
The cubic Szegő equation. (L’équation de Szegő cubique.) Zbl 1228.35225
Gérard, Patrick; Grellier, Sandrine
58
2010
Nonlinear Schrödinger equation on four-dimensional compact manifolds. Zbl 1183.35251
Gérard, Patrick; Pierfelice, Vittoria
7
2010
The cubic Szegö equation. (L’equation de Szegö cubique.) Zbl 1213.35397
Gérard, Patrick; Grellier, Sandrine
3
2010
A mean-field toy model for resonant transport. Zbl 1194.35462
Gerard, Patrick; Pallard, Christophe
2
2010
Orbital stability of traveling waves for the one-dimensional Gross-Pitaevskii equation. Zbl 1232.35152
Gérard, Patrick; Zhang, Zhifei
21
2009
The Gross-Pitaevskii equation in the energy space. Zbl 1166.35373
Gérard, Patrick
22
2008
Pseudo-differential operators and the Nash–Moser theorem. Transl. from the French by Stephen S. Wilson. Zbl 1121.47033
Alinhac, Serge; Gérard, Patrick
77
2007
Restrictions of the Laplace-Beltrami eigenfunctions to submanifolds. Zbl 1131.35053
Burq, N.; Gérard, P.; Tzvetkov, N.
73
2007
Global solutions for the nonlinear Schrödinger equation on three-dimensional compact manifolds. Zbl 1180.35475
Burq, N.; Gérard, P.; Tzvetkov, N.
14
2007
Stabilization and control for the nonlinear Schrödinger equation on a compact surface. Zbl 1127.93015
Dehman, B.; Gérard, P.; Lebeau, G.
58
2006
The Cauchy problem for the Gross–Pitaevskii equation. Zbl 1122.35133
Gérard, P.
48
2006
Nonlinear Schrödinger equations in inhomogeneous media: wellposedness and illposedness of the Cauchy problem. Zbl 1106.35096
Gérard, Patrick
9
2006
Bilinear eigenfunction estimates and the nonlinear Schrödinger equation on surfaces. Zbl 1092.35099
Burq, N.; Gérard, P.; Tzvetkov, N.
75
2005
Multilinear eigenfunction estimates and global existence for the three dimensional nonlinear Schrödinger equations. Zbl 1116.35109
Burq, Nicolas; Gérard, Patrick; Tzvetkov, Nikolay
54
2005
Nonlinear Schrödinger equations on compact manifolds. Zbl 1076.35115
Gérard, P.
4
2005
Strichartz inequalities and the nonlinear Schrödinger equation on compact manifolds. Zbl 1067.58027
Burq, N.; Gérard, P.; Tzvetkov, N.
198
2004
On nonlinear Schrödinger equations in exterior domains. Zbl 1061.35126
Burq, N.; Gérard, P.; Tzvetkov, N.
44
2004
Multilinear estimates for the Laplace spectral projectors on compact manifolds. Zbl 1040.58011
Burq, Nicolas; Gérard, Patrick; Tzvetkov, Nikolay
8
2004
The Cauchy problem for the nonlinear Schrödinger equation on compact manifolds. Zbl 1084.35086
Burq, N.; Gérard, P.; Tzvetkov, N.
5
2004
Two-scale Wigner measures and the Landau-Zener formulas. Zbl 1322.81059
Kammerer, C. Fermanian; Gérard, P.
1
2004
A Landau-Zener formula for two-scaled Wigner measures. Zbl 1145.81368
Fermanian Kammerer, Clotilde; Gerard, Patrick
1
2004
A Landau-Zener formula for non-degenerated involutive codimension 3 crossings. Zbl 1049.81029
Fermanian Kammerer, Clotilde; Gérard, Patrick
28
2003
Two singular dynamics of the nonlinear Schrödinger equation on a plane domain. Zbl 1044.35084
Burq, N.; Gérard, P.; Tzvetkov, N.
25
2003
The Cauchy problem for the nonlinear Schrödinger equation on a compact manifold. Zbl 1362.35282
Burq, Nicolas; Gérard, Patrick; Tzvetkov, Nikolay
10
2003
An example of singular dynamics for the nonlinear Schrödinger equation on bounded domains. Zbl 1210.35225
Burg, N.; Gérard, P.; Tzvetkov, N.
1
2003
An instability property of the nonlinear Schrödinger equation on \(S^d\). Zbl 1003.35113
Burq, N.; Gérard, P.; Tzvetkov, N.
58
2002
Semi-classical measures and eigenvalue crossings. (Mesures semi-classiques et croisement de modes.) Zbl 0996.35004
Fermanian-Kammerer, Clotilde; Gérard, Patrick
39
2002
A Landau-Zener formula for a generic crossing in codimension 2. (Une formule de Landau-Zener pour un croisement générique de codimension 2.) Zbl 1292.35252
Fermanian Kammerer, Clotilde; Gérard, Patrick
2
2002
Profile decomposition for the wave equation outside a convex obstacle. Zbl 0980.35088
Gallagher, Isabelle; Gérard, Patrick
14
2001
The Schrödinger equation on a compact manifold: Strichartz estimates and applications. Zbl 1043.58019
Burq, Nicolas; Gérard, Patrick; Tzvetkov, Nikolay
5
2001
Besov spaces and Strichartz estimates on the Heisenberg group. (Espaces de Besov et estimations de Strichartz généralisées sur le groupe de Heisenberg.) Zbl 0965.22010
Bahouri, Hajer; Gérard, Patrick; Xu, Chao-Jiang
44
2000
Sensitivity phenomena for certain thin elastic shells with edges. Zbl 0989.74047
Gerard, Patrick; Sanchez-Palencia, Evariste
5
2000
Semiclassical measures and crossing of modes. (Mesures semi-classiques et croisement de modes.) Zbl 1055.81534
Fermanian Kammerer, Clotilde; Gerard, Patrick
3
2000
High frequency approximation of solutions to critical nonlinear wave equations. Zbl 0919.35089
Bahouri, Hajer; Gérard, Patrick
208
1999
Description of the lack of compactness for the Sobolev imbedding. Zbl 0907.46027
Gérard, P.
70
1998
Homogenization limits and Wigner transforms. Zbl 0881.35099
Gérard, Patrick; Markowich, Peter A.; Mauser, Norbert J.; Poupaud, Frédéric
209
1997
A necessary and sufficient condition for the exact controllability of the wave equation. (Condition nécessaire et suffisante pour la contrôlabilité exacte des ondes.) Zbl 0906.93008
Burq, Nicolas; Gérard, Patrick
100
1997
Sharp Sobolev inequalities. (Inégalités de Sobolev précisées.) Zbl 1066.46501
Gerard, Patrick; Meyer, Yves; Oru, Frédérique
41
1997
Concentration effects in critical nonlinear wave equation and scattering theory. Zbl 0926.35090
Bahouri, Hajer; Gérard, Patrick
3
1997
Generalized geometric optics for critical nonlinear waves. (Optique géométrique généralisée pour les ondes non linéaires critiques.) Zbl 1068.35522
Bahouri, Hajer; Gerard, Patrick
1
1997
Oscillations of concentration effects in semilinear dispersive wave equations. Zbl 0868.35075
Gérard, Patrick
42
1996
A microlocal version of concentration-compactness. Zbl 0868.35005
Gérard, Patrick
2
1996
A compactness result for generalized Radon transforms. Zbl 0864.44001
Gérard, Patrick; Golse, François; Wennberg, Bernt
2
1996
Ergodic properties of eigenfunctions for the Dirichlet problem. Zbl 0788.35103
Gérard, Patrick; Leichtnam, Eric
99
1993
Diffraction of a wave at a corner. (Diffusion d’une onde par un coin.) Zbl 0779.35063
Gérard, Patrick; Lebeau, Gilles
14
1993
Remarks on the semiclassical analysis of the nonlinear Schrödinger equation. (Remarques sur l’analyse semi-classique de l’équation de Schrödinger non linéaire.) Zbl 0874.35111
Gérard, Patrick
7
1993
Averaging regularity results for PDEs under transversality assumptions. Zbl 0832.35020
Gérard, Patrick; Golse, François
16
1992
Recent results concerning two-dimensional incompressible perfect fluids (after J.-Y. Chemin and J.-M. Delort). (Résultats récents sur les fluides parfaits incompressibles bidimensionnels (d’après J.-Y. Chemin et J.-M. Delort).) Zbl 1154.76321
Gérard, Patrick
9
1992
Microlocal defect measures. Zbl 0770.35001
Gérard, Patrick
205
1991
Pseudo-differential operators and the Nash-Moser theorem. (Opérateurs pseudo-différentiels et théorème de Nash-Moser.) Zbl 0791.47044
Alinhac, Serge; Gérard, Patrick
87
1991
Mesures semi-classiques et ondes de Bloch. (Semiclassical measures and Bloch waves). Zbl 0739.35096
Gérard, P.
30
1991
Moyennisation et régularité deux-microlocale. (Second microlocal averaging and regularity). Zbl 0725.35003
Gérard, Patrick
16
1990
Compacité par compensation et régularité 2-microlocale. (Compensated compactness and 2-microlocal regularity). Zbl 0707.35032
Gérard, P.
2
1989
Solutions conormales analytiques d’équations hyperboliques non linéaires. (Conormal analytic solutions of nonlinear hyperbolic equations). Zbl 0639.35054
Gerard, Patrick
3
1988
Solutions globales du problème de Cauchy pour l’équation de Boltzmann [d’après R. J. Di Perna et P. L. Lions]. Zbl 0704.76041
Gérard, Patrick
1
1988
Regularization by averaging for solutions of partial differential equations. Zbl 0724.35115
Gérard, P.
1
1988
Propagation de la régularité locale de solutions d’équations hyperboliques non linéaires. (Propagation of local smoothness for solutions of nonlinear hyperbolic equations). Zbl 0617.35079
Gerard, P.; Rauch, J.
8
1987
Moyennes de solutions d’équations aux dérivées partielles. (Means of solutions of partial differential equations). Zbl 0657.35020
Gerard, P.
3
1987
Régularité de moyennes de solutions d’équations aux dérivées partielles. (Regularity of means of solutions of partial differential equations). Zbl 0639.35010
Gerard, Patrick
1
1987
all top 5

Cited by 1,458 Authors

40 Gerard, Patrick
39 Tzvetkov, Nikolay
35 Burq, Nicolas
28 Fermanian-Kammerer, Clotilde
27 Carles, Rémi
25 Cavalcanti, Marcelo Moreira
23 Kenig, Carlos Eduardo
21 Duyckaerts, Thomas
20 Domingos Cavalcanti, Valéria Neves
19 Bahouri, Hajer
19 Bal, Guillaume
17 Jin, Shi
16 Gallagher, Isabelle
15 Markowich, Peter Alexander
15 Merle, Frank
15 Oh, Tadahiro
15 Paul, Thierry
15 Ryzhik, Lenya
15 Visciglia, Nicola
14 Nakanishi, Kenji
14 Thomann, Laurent
14 Zuazua, Enrique
13 Panov, Evgeniy Yu.
12 Antonić, Nenad
12 Léautaud, Matthieu
12 Macià, Fabricio
12 Miao, Changxing
12 Mitrovic, Darko
11 Galkowski, Jeffrey
11 Laurent, Camille
11 Lawrie, Andrew G. W.
11 Lebeau, Gilles
11 Mauser, Norbert Julius
11 Tataru, Daniel
10 Gala, Sadek
10 Ibrahim, Slim
10 Krieger, Joachim
10 Masmoudi, Nader
10 Perthame, Benoît
10 Raphael, Pierre
10 Sun, Chenmin
10 Trélat, Emmanuel
9 Allaire, Grégoire
9 Banica, Valeria
9 Evnin, Oleg
9 Guo, Zihua
9 Hani, Zaher
9 Israwi, Samer
9 Lasser, Caroline
9 Lazar, Martin
9 Planchon, Fabrice
9 Saut, Jean-Claude
9 Schlag, Wilhelm
9 Sogge, Christopher D.
9 Sparber, Christof
9 Tacy, Melissa
9 Toth, John Andrew
9 Visan, Monica
8 Aloui, Lassaad
8 Ervedoza, Sylvain
8 Gravejat, Philippe
8 Grellier, Sandrine
8 Hassell, Andrew
8 Majdoub, Mohamed
8 Pausader, Benoît
8 Pinaud, Olivier
8 Xu, Guixiang
8 Zelditch, Steve
7 Alabau-Boussouira, Fatiha
7 Bao, Weizhu
7 Blair, Matthew D.
7 Brzeźniak, Zdzisław
7 Christianson, Hans
7 Corrêa, Wellington José
7 Gassot, Louise
7 Germain, Pierre
7 Gonzalez Martinez, Victor Hugo
7 Guardia, Marcel
7 Killip, Rowan
7 Kwon, Soonsik
7 Pierfelice, Vittoria
7 Pocovnicu, Oana
7 Privat, Yannick
7 Ragusa, Maria Alessandra
7 Rosier, Lionel
7 Soler, Juan S.
7 Wang, Tao
6 Alazard, Thomas
6 Athanassoulis, Agisillaos
6 Bardos, Claude Williams
6 Chemin, Jean-Yves
6 de Laire, André
6 Erceg, Marko
6 Golse, François
6 Herr, Sebastian
6 Jendrej, Jacek
6 Keraani, Sahbi
6 Komorowski, Tomasz
6 Lee, Sanghyuk
6 Lenzmann, Enno
...and 1,358 more Authors
all top 5

Cited in 270 Serials

78 Journal of Differential Equations
71 Communications in Mathematical Physics
69 Communications in Partial Differential Equations
63 Journal of Functional Analysis
49 Archive for Rational Mechanics and Analysis
47 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire
42 Journal de Mathématiques Pures et Appliquées. Neuvième Série
32 Transactions of the American Mathematical Society
31 Journal of Mathematical Physics
29 Journal of Mathematical Analysis and Applications
28 SIAM Journal on Mathematical Analysis
27 Comptes Rendus. Mathématique. Académie des Sciences, Paris
24 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods
22 Discrete and Continuous Dynamical Systems
22 Analysis & PDE
21 Duke Mathematical Journal
19 Journal of Computational Physics
19 Mathematische Annalen
19 Journal of the European Mathematical Society (JEMS)
18 Communications on Pure and Applied Analysis
17 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations
17 Séminaire Laurent Schwartz. EDP et Applications
16 Bulletin de la Société Mathématique de France
16 Inventiones Mathematicae
16 Proceedings of the American Mathematical Society
16 Journal of Hyperbolic Differential Equations
15 Nonlinearity
15 Advances in Mathematics
14 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences
13 Communications on Pure and Applied Mathematics
13 ZAMP. Zeitschrift für angewandte Mathematik und Physik
13 Annales de l’Institut Fourier
13 The Journal of Geometric Analysis
13 Communications in Contemporary Mathematics
12 Revista Matemática Iberoamericana
12 Pure and Applied Analysis
11 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série
11 Physica D
11 Annales Henri Poincaré
10 Mathematische Zeitschrift
10 Journal of the American Mathematical Society
10 Journal of Dynamics and Differential Equations
10 Science China. Mathematics
10 Journal of Spectral Theory
9 Journal d’Analyse Mathématique
9 Annali di Matematica Pura ed Applicata. Serie Quarta
9 Asymptotic Analysis
9 NoDEA. Nonlinear Differential Equations and Applications
9 Journal of Pseudo-Differential Operators and Applications
8 Wave Motion
8 SIAM Journal on Control and Optimization
8 Geometric and Functional Analysis. GAFA
8 Calculus of Variations and Partial Differential Equations
8 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis
8 Annals of PDE
7 Numerische Mathematik
7 Journal of Scientific Computing
7 Journal of Mathematical Sciences (New York)
7 The Journal of Fourier Analysis and Applications
7 Journal of Evolution Equations
7 Evolution Equations and Control Theory
7 Journal de l’École Polytechnique – Mathématiques
6 Applicable Analysis
6 Journal of Statistical Physics
6 Transport Theory and Statistical Physics
6 Forum Mathematicum
6 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI
6 M2AN. Mathematical Modelling and Numerical Analysis. ESAIM, European Series in Applied and Industrial Mathematics
6 Multiscale Modeling & Simulation
6 Discrete and Continuous Dynamical Systems. Series S
6 Stochastic and Partial Differential Equations. Analysis and Computations
6 Annales Henri Lebesgue
5 Memoirs of the American Mathematical Society
5 Quarterly of Applied Mathematics
5 Bulletin of the American Mathematical Society. New Series
5 Acta Mathematica Sinica. English Series
5 Journal of the Institute of Mathematics of Jussieu
5 Acta Numerica
5 Journal of Physics A: Mathematical and Theoretical
4 Mathematical Methods in the Applied Sciences
4 American Journal of Mathematics
4 Applied Mathematics and Optimization
4 Proceedings of the London Mathematical Society. Third Series
4 Chinese Annals of Mathematics. Series B
4 Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni
4 SIAM Journal on Applied Mathematics
4 Journal of Nonlinear Science
4 Nonlinear Analysis. Real World Applications
4 Foundations of Computational Mathematics
4 Milan Journal of Mathematics
4 Oberwolfach Reports
4 Mathematical Control and Related Fields
4 Tunisian Journal of Mathematics
3 Israel Journal of Mathematics
3 Letters in Mathematical Physics
3 Journal of Computational and Applied Mathematics
3 Journal of Differential Geometry
3 Journal of the London Mathematical Society. Second Series
3 Journal of the Mathematical Society of Japan
3 Journal of Optimization Theory and Applications
...and 170 more Serials
all top 5

Cited in 53 Fields

1,364 Partial differential equations (35-XX)
238 Quantum theory (81-XX)
198 Global analysis, analysis on manifolds (58-XX)
177 Fluid mechanics (76-XX)
165 Dynamical systems and ergodic theory (37-XX)
121 Systems theory; control (93-XX)
118 Statistical mechanics, structure of matter (82-XX)
100 Operator theory (47-XX)
90 Harmonic analysis on Euclidean spaces (42-XX)
84 Numerical analysis (65-XX)
83 Functional analysis (46-XX)
66 Mechanics of deformable solids (74-XX)
54 Probability theory and stochastic processes (60-XX)
47 Optics, electromagnetic theory (78-XX)
46 Calculus of variations and optimal control; optimization (49-XX)
43 Differential geometry (53-XX)
29 Ordinary differential equations (34-XX)
28 Topological groups, Lie groups (22-XX)
23 Abstract harmonic analysis (43-XX)
19 Real functions (26-XX)
16 Number theory (11-XX)
14 Relativity and gravitational theory (83-XX)
13 Functions of a complex variable (30-XX)
11 Special functions (33-XX)
10 Integral equations (45-XX)
9 Measure and integration (28-XX)
9 Geophysics (86-XX)
8 General and overarching topics; collections (00-XX)
8 Mechanics of particles and systems (70-XX)
8 Biology and other natural sciences (92-XX)
7 Potential theory (31-XX)
7 Approximations and expansions (41-XX)
7 Integral transforms, operational calculus (44-XX)
6 Linear and multilinear algebra; matrix theory (15-XX)
5 Information and communication theory, circuits (94-XX)
4 Classical thermodynamics, heat transfer (80-XX)
4 Astronomy and astrophysics (85-XX)
3 Group theory and generalizations (20-XX)
3 Several complex variables and analytic spaces (32-XX)
3 General topology (54-XX)
3 Operations research, mathematical programming (90-XX)
2 Combinatorics (05-XX)
2 Nonassociative rings and algebras (17-XX)
2 Difference and functional equations (39-XX)
2 Statistics (62-XX)
2 Game theory, economics, finance, and other social and behavioral sciences (91-XX)
1 History and biography (01-XX)
1 Algebraic geometry (14-XX)
1 Associative rings and algebras (16-XX)
1 Sequences, series, summability (40-XX)
1 Geometry (51-XX)
1 Manifolds and cell complexes (57-XX)
1 Computer science (68-XX)

Citations by Year

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