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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
Videos: carmin.tv
Member of Collective: Bourbaki, Nicolas
all top 5

Serials

12 Séminaire Équations aux Dérivées Partielles
5 Séminaire Laurent Schwartz. EDP et Applications
4 Communications on Pure and Applied Mathematics
4 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série
3 Inventiones Mathematicae
3 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire
3 Comptes Rendus. Mathématique. Académie des Sciences, Paris
2 Archive for Rational Mechanics and Analysis
2 Journal d’Analyse Mathématique
2 American Journal of Mathematics
2 Bulletin de la Société Mathématique de France
2 Duke Mathematical Journal
2 Journal of Functional Analysis
2 Mathematische Zeitschrift
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 Tunisian Journal of Mathematics
1 Communications in Mathematical Physics
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 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

97 Publications have been cited 2,973 times in 1,924 Documents Cited by Year
Microlocal defect measures. Zbl 0770.35001
Gérard, Patrick
231
1991
Strichartz inequalities and the nonlinear Schrödinger equation on compact manifolds. Zbl 1067.58027
Burq, N.; Gérard, P.; Tzvetkov, N.
227
2004
High frequency approximation of solutions to critical nonlinear wave equations. Zbl 0919.35089
Bahouri, Hajer; Gérard, Patrick
225
1999
Homogenization limits and Wigner transforms. Zbl 0881.35099
Gérard, Patrick; Markowich, Peter A.; Mauser, Norbert J.; Poupaud, Frédéric
219
1997
Description of the lack of compactness for the Sobolev imbedding. Zbl 0907.46027
Gérard, P.
129
1998
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
123
1997
Ergodic properties of eigenfunctions for the Dirichlet problem. Zbl 0788.35103
Gérard, Patrick; Leichtnam, Eric
109
1993
Pseudo-differential operators and the Nash-Moser theorem. (Opérateurs pseudo-différentiels et théorème de Nash-Moser.) Zbl 0791.47044
Alinhac, Serge; Gérard, Patrick
105
1991
Pseudo-differential operators and the Nash–Moser theorem. Transl. from the French by Stephen S. Wilson. Zbl 1121.47033
Alinhac, Serge; Gérard, Patrick
96
2007
Bilinear eigenfunction estimates and the nonlinear Schrödinger equation on surfaces. Zbl 1092.35099
Burq, N.; Gérard, P.; Tzvetkov, N.
85
2005
The cubic Szegő equation. (L’équation de Szegő cubique.) Zbl 1228.35225
Gérard, Patrick; Grellier, Sandrine
75
2010
Restrictions of the Laplace-Beltrami eigenfunctions to submanifolds. Zbl 1131.35053
Burq, N.; Gérard, P.; Tzvetkov, N.
74
2007
Stabilization and control for the nonlinear Schrödinger equation on a compact surface. Zbl 1127.93015
Dehman, B.; Gérard, P.; Lebeau, G.
69
2006
An instability property of the nonlinear Schrödinger equation on \(S^d\). Zbl 1003.35113
Burq, N.; Gérard, P.; Tzvetkov, N.
64
2002
Multilinear eigenfunction estimates and global existence for the three dimensional nonlinear Schrödinger equations. Zbl 1116.35109
Burq, Nicolas; Gérard, Patrick; Tzvetkov, Nikolay
59
2005
The Cauchy problem for the Gross–Pitaevskii equation. Zbl 1122.35133
Gérard, P.
57
2006
Sharp Sobolev inequalities. (Inégalités de Sobolev précisées.) Zbl 1066.46501
Gerard, Patrick; Meyer, Yves; Oru, Frédérique
52
1997
Mesures semi-classiques et ondes de Bloch. (Semiclassical measures and Bloch waves). Zbl 0739.35096
Gérard, P.
49
1991
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
49
2000
Effective integrable dynamics for a certain nonlinear wave equation. Zbl 1268.35013
Gérard, Patrick; Grellier, Sandrine
49
2012
On nonlinear Schrödinger equations in exterior domains. Zbl 1061.35126
Burq, N.; Gérard, P.; Tzvetkov, N.
47
2004
Oscillations of concentration effects in semilinear dispersive wave equations. Zbl 0868.35075
Gérard, Patrick
46
1996
Semi-classical measures and eigenvalue crossings. (Mesures semi-classiques et croisement de modes.) Zbl 0996.35004
Fermanian-Kammerer, Clotilde; Gérard, Patrick
42
2002
The cubic Szegő equation and Hankel operators. Zbl 1410.37001
Gérard, Patrick; Grellier, Sandrine
39
2017
An explicit formula for the cubic Szegő equation. Zbl 1318.37024
Gérard, Patrick; Grellier, Sandrine
34
2015
Invariant tori for the cubic Szegö equation. Zbl 1252.35026
Gérard, Patrick; Grellier, Sandrine
33
2012
The Gross-Pitaevskii equation in the energy space. Zbl 1166.35373
Gérard, Patrick
28
2008
A Landau-Zener formula for non-degenerated involutive codimension 3 crossings. Zbl 1049.81029
Fermanian Kammerer, Clotilde; Gérard, Patrick
28
2003
On the integrability of the Benjamin-Ono equation on the torus. Zbl 1471.35354
Gérard, Patrick; Kappeler, Thomas
27
2021
Two singular dynamics of the nonlinear Schrödinger equation on a plane domain. Zbl 1044.35084
Burq, N.; Gérard, P.; Tzvetkov, N.
26
2003
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
26
2018
Orbital stability of traveling waves for the one-dimensional Gross-Pitaevskii equation. Zbl 1232.35152
Gérard, Patrick; Zhang, Zhifei
25
2009
On the radius of analyticity of solutions to the cubic Szegő equation. Zbl 1332.35058
Gérard, Patrick; Guo, Yanqiu; Titi, Edriss S.
18
2015
On the cubic lowest Landau level equation. Zbl 1412.82034
Gérard, Patrick; Germain, Pierre; Thomann, Laurent
18
2019
Moyennisation et régularité deux-microlocale. (Second microlocal averaging and regularity). Zbl 0725.35003
Gérard, Patrick
17
1990
Averaging regularity results for PDEs under transversality assumptions. Zbl 0832.35020
Gérard, Patrick; Golse, François
17
1992
Global solutions for the nonlinear Schrödinger equation on three-dimensional compact manifolds. Zbl 1180.35475
Burq, N.; Gérard, P.; Tzvetkov, N.
17
2007
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
17
1993
On the spectrum of the Lax operator of the Benjamin-Ono equation on the torus. Zbl 1452.37070
Gérard, Patrick; Kappeler, Thomas; Topalov, Petar
16
2020
Profile decomposition for the wave equation outside a convex obstacle. Zbl 0980.35088
Gallagher, Isabelle; Gérard, Patrick
15
2001
Diffraction of a wave at a corner. (Diffusion d’une onde par un coin.) Zbl 0779.35063
Gérard, Patrick; Lebeau, Gilles
13
1993
A Lax pair structure for the half-wave maps equation. Zbl 1393.37074
Gérard, Patrick; Lenzmann, Enno
12
2018
Nonlinear Schrödinger equation on four-dimensional compact manifolds. Zbl 1183.35251
Gérard, Patrick; Pierfelice, Vittoria
11
2010
The Cauchy problem for the nonlinear Schrödinger equation on a compact manifold. Zbl 1362.35282
Burq, Nicolas; Gérard, Patrick; Tzvetkov, Nikolay
11
2003
Sharp well-posedness results of the Benjamin-Ono equation in \(H^s(\mathbb{T},\mathbb{R})\) and qualitative properties of its solutions. Zbl 1533.35061
Gérard, Patrick; Kappeler, Thomas; Topalov, Peter
11
2023
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
10
1992
Nonlinear Schrödinger equations in inhomogeneous media: wellposedness and illposedness of the Cauchy problem. Zbl 1106.35096
Gérard, Patrick
10
2006
Stabilization of wave equations on the torus with rough dampings. Zbl 1462.35070
Burq, Nicolas; Gérard, Patrick
10
2020
An explicit formula for the Benjamin-Ono equation. Zbl 1531.37066
Gérard, Patrick
10
2023
Wigner measure propagation and conical singularity for general initial data. Zbl 1288.35408
Fermanian-Kammerer, Clotilde; Gérard, Patrick; Lasser, Caroline
9
2013
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.
9
1987
An inverse problem for self-adjoint positive Hankel operators. Zbl 1338.47024
Gérard, Patrick; Pushnitski, Alexander
8
2015
Multilinear estimates for the Laplace spectral projectors on compact manifolds. Zbl 1040.58011
Burq, Nicolas; Gérard, Patrick; Tzvetkov, Nikolay
8
2004
Unbounded Hankel operators and the flow of the cubic Szegő equation. Zbl 1525.47058
Gérard, Patrick; Pushnitski, Alexander
7
2023
On the Benjamin-Ono equation on \(\mathbb{T}\) and its periodic and quasiperiodic solutions. Zbl 1495.37060
Gérard, Patrick; Kappeler, Thomas; Topalov, Petar
7
2022
The cubic Szegő flow at low regularity. Zbl 1475.35434
Gérard, Patrick; Koch, Herbert
7
2017
On the analytic Birkhoff normal form of the Benjamin-Ono equation and applications. Zbl 1521.37085
Gérard, Patrick; Kappeler, Thomas; Topalov, Petar
7
2022
Inverse spectral problems for compact Hankel operators. Zbl 1304.47038
Gérard, Patrick; Grellier, Sandrine
6
2014
The cubic Szegö equation. (L’equation de Szegö cubique.) Zbl 1213.35397
Gérard, Patrick; Grellier, Sandrine
6
2010
A drift homogenization problem revisited. Zbl 1270.35058
Briane, Marc; Gérard, Patrick
6
2012
The Schrödinger equation on a compact manifold: Strichartz estimates and applications. Zbl 1043.58019
Burq, Nicolas; Gérard, Patrick; Tzvetkov, Nikolay
6
2001
Weighted model spaces and Schmidt subspaces of Hankel operators. Zbl 1448.47040
Gérard, Patrick; Pushnitski, Alexander
6
2020
Sensitivity phenomena for certain thin elastic shells with edges. Zbl 0989.74047
Gerard, Patrick; Sanchez-Palencia, Evariste
5
2000
Nonlinear Schrödinger equations on compact manifolds. Zbl 1076.35115
Gérard, P.
5
2005
The Cauchy problem for the nonlinear Schrödinger equation on compact manifolds. Zbl 1084.35086
Burq, N.; Gérard, P.; Tzvetkov, N.
5
2004
The Calogero-Moser derivative nonlinear Schrödinger equation. Zbl 07896921
Gérard, Patrick; Lenzmann, Enno
5
2024
Inverse spectral theory for a class of non-compact Hankel operators. Zbl 07036937
Gérard, Patrick; Pushnitski, Alexander
5
2019
On the growth of Sobolev norms for the cubic Szegő equation. Zbl 1355.35022
Gérard, Patrick; Grellier, Sandrine
4
2016
Compacité par compensation et régularité 2-microlocale. (Compensated compactness and 2-microlocal regularity). Zbl 0707.35032
Gérard, P.
3
1989
Concentration effects in critical nonlinear wave equation and scattering theory. Zbl 0926.35090
Bahouri, Hajer; Gérard, Patrick
3
1997
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
The Schrödinger-Poisson system on the sphere. Zbl 1231.35229
Gérard, Patrick; Méhats, Florian
3
2011
Semiclassical measures and crossing of modes. (Mesures semi-classiques et croisement de modes.) Zbl 1055.81534
Fermanian Kammerer, Clotilde; Gerard, Patrick
3
2000
The zero dispersion limit for the Benjamin-Ono equation on the line. (Limite à faible dispersion pour l’équation de Benjamin-Ono sur la droite.) Zbl 07887262
Gérard, Patrick
3
2024
The cubic Szegő equation on the real line: explicit formula and well-posedness on the Hardy class. Zbl 07877943
Gérard, Patrick; Pushnitski, Alexander
3
2024
On a damped Szegö equation (with an appendix in collaboration with Christian Klein). Zbl 1448.35022
Gérard, Patrick; Grellier, Sandrine
3
2020
A nonlinear Fourier transform for the Benjamin-Ono equation on the torus and applications. Zbl 1479.35020
Gérard, Patrick
3
2020
A compactness result for generalized Radon transforms. Zbl 0864.44001
Gérard, Patrick; Golse, François; Wennberg, Bernt
2
1996
A microlocal version of concentration-compactness. Zbl 0868.35005
Gérard, Patrick
2
1996
Régularité de moyennes de solutions d’équations aux dérivées partielles. (Regularity of means of solutions of partial differential equations). Zbl 0639.35010
Gerard, Patrick
2
1987
A mean-field toy model for resonant transport. Zbl 1194.35462
Gerard, Patrick; Pallard, Christophe
2
2010
A survey of the Szegő equation. Zbl 1428.35067
Gérard, Patrick; Grellier, Sandrine
2
2019
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
The structure of Schmidt subspaces of Hankel operators: a short proof. Zbl 1514.47053
Gérard, Patrick; Pushnitski, Alexander
2
2021
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
A Landau-Zener formula for two-scaled Wigner measures. Zbl 1145.81368
Fermanian Kammerer, Clotilde; Gerard, Patrick
1
2004
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
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 Strichartz estimates on the Heisenberg group. (Estimation de Strichartz généralisées sur le groupe de Heisenberg.) Zbl 1104.35303
Bahouri, Hajer; Gerard, Patrick; Xu, Chao-Jiang
1
1998
A Nekhoroshev theorem for some perturbations of the Benjamin-Ono equation with initial data close to finite gap tori. Zbl 07873282
Bambusi, Dario; Gérard, Patrick
1
2024
An introduction to the cubic Szegö equation. Zbl 1348.35232
Gérard, Patrick
1
2013
Two-scale Wigner measures and the Landau-Zener formulas. Zbl 1322.81059
Kammerer, C. Fermanian; Gérard, P.
1
2004
Inverse spectral problem for a pair of self-adjoint Hankel operators. Zbl 1449.35032
Gérard, Patrick; Grellier, Sandrine
1
2017
Generic colourful tori and inverse spectral transform for Hankel operators. Zbl 1409.35045
Gérard, Patrick; Grellier, Sandrine
1
2019
The Calogero-Moser derivative nonlinear Schrödinger equation. Zbl 07896921
Gérard, Patrick; Lenzmann, Enno
5
2024
The zero dispersion limit for the Benjamin-Ono equation on the line. (Limite à faible dispersion pour l’équation de Benjamin-Ono sur la droite.) Zbl 07887262
Gérard, Patrick
3
2024
The cubic Szegő equation on the real line: explicit formula and well-posedness on the Hardy class. Zbl 07877943
Gérard, Patrick; Pushnitski, Alexander
3
2024
A Nekhoroshev theorem for some perturbations of the Benjamin-Ono equation with initial data close to finite gap tori. Zbl 07873282
Bambusi, Dario; Gérard, Patrick
1
2024
Sharp well-posedness results of the Benjamin-Ono equation in \(H^s(\mathbb{T},\mathbb{R})\) and qualitative properties of its solutions. Zbl 1533.35061
Gérard, Patrick; Kappeler, Thomas; Topalov, Peter
11
2023
An explicit formula for the Benjamin-Ono equation. Zbl 1531.37066
Gérard, Patrick
10
2023
Unbounded Hankel operators and the flow of the cubic Szegő equation. Zbl 1525.47058
Gérard, Patrick; Pushnitski, Alexander
7
2023
On the Benjamin-Ono equation on \(\mathbb{T}\) and its periodic and quasiperiodic solutions. Zbl 1495.37060
Gérard, Patrick; Kappeler, Thomas; Topalov, Petar
7
2022
On the analytic Birkhoff normal form of the Benjamin-Ono equation and applications. Zbl 1521.37085
Gérard, Patrick; Kappeler, Thomas; Topalov, Petar
7
2022
On the integrability of the Benjamin-Ono equation on the torus. Zbl 1471.35354
Gérard, Patrick; Kappeler, Thomas
27
2021
The structure of Schmidt subspaces of Hankel operators: a short proof. Zbl 1514.47053
Gérard, Patrick; Pushnitski, Alexander
2
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
16
2020
Stabilization of wave equations on the torus with rough dampings. Zbl 1462.35070
Burq, Nicolas; Gérard, Patrick
10
2020
Weighted model spaces and Schmidt subspaces of Hankel operators. Zbl 1448.47040
Gérard, Patrick; Pushnitski, Alexander
6
2020
On a damped Szegö equation (with an appendix in collaboration with Christian Klein). Zbl 1448.35022
Gérard, Patrick; Grellier, Sandrine
3
2020
A nonlinear Fourier transform for the Benjamin-Ono equation on the torus and applications. Zbl 1479.35020
Gérard, Patrick
3
2020
On the cubic lowest Landau level equation. Zbl 1412.82034
Gérard, Patrick; Germain, Pierre; Thomann, Laurent
18
2019
Inverse spectral theory for a class of non-compact Hankel operators. Zbl 07036937
Gérard, Patrick; Pushnitski, Alexander
5
2019
A survey of the Szegő equation. Zbl 1428.35067
Gérard, Patrick; Grellier, Sandrine
2
2019
Wave turbulence and complete integrability. Zbl 1442.35419
Gérard, Patrick
2
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
26
2018
A Lax pair structure for the half-wave maps equation. Zbl 1393.37074
Gérard, Patrick; Lenzmann, Enno
12
2018
The cubic Szegő equation and Hankel operators. Zbl 1410.37001
Gérard, Patrick; Grellier, Sandrine
39
2017
The cubic Szegő flow at low regularity. Zbl 1475.35434
Gérard, Patrick; Koch, Herbert
7
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
4
2016
An explicit formula for the cubic Szegő equation. Zbl 1318.37024
Gérard, Patrick; Grellier, Sandrine
34
2015
On the radius of analyticity of solutions to the cubic Szegő equation. Zbl 1332.35058
Gérard, Patrick; Guo, Yanqiu; Titi, Edriss S.
18
2015
An inverse problem for self-adjoint positive Hankel operators. Zbl 1338.47024
Gérard, Patrick; Pushnitski, Alexander
8
2015
Inverse spectral problems for compact Hankel operators. Zbl 1304.47038
Gérard, Patrick; Grellier, Sandrine
6
2014
Wigner measure propagation and conical singularity for general initial data. Zbl 1288.35408
Fermanian-Kammerer, Clotilde; Gérard, Patrick; Lasser, Caroline
9
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
49
2012
Invariant tori for the cubic Szegö equation. Zbl 1252.35026
Gérard, Patrick; Grellier, Sandrine
33
2012
A drift homogenization problem revisited. Zbl 1270.35058
Briane, Marc; Gérard, Patrick
6
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
75
2010
Nonlinear Schrödinger equation on four-dimensional compact manifolds. Zbl 1183.35251
Gérard, Patrick; Pierfelice, Vittoria
11
2010
The cubic Szegö equation. (L’equation de Szegö cubique.) Zbl 1213.35397
Gérard, Patrick; Grellier, Sandrine
6
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
25
2009
The Gross-Pitaevskii equation in the energy space. Zbl 1166.35373
Gérard, Patrick
28
2008
Pseudo-differential operators and the Nash–Moser theorem. Transl. from the French by Stephen S. Wilson. Zbl 1121.47033
Alinhac, Serge; Gérard, Patrick
96
2007
Restrictions of the Laplace-Beltrami eigenfunctions to submanifolds. Zbl 1131.35053
Burq, N.; Gérard, P.; Tzvetkov, N.
74
2007
Global solutions for the nonlinear Schrödinger equation on three-dimensional compact manifolds. Zbl 1180.35475
Burq, N.; Gérard, P.; Tzvetkov, N.
17
2007
Stabilization and control for the nonlinear Schrödinger equation on a compact surface. Zbl 1127.93015
Dehman, B.; Gérard, P.; Lebeau, G.
69
2006
The Cauchy problem for the Gross–Pitaevskii equation. Zbl 1122.35133
Gérard, P.
57
2006
Nonlinear Schrödinger equations in inhomogeneous media: wellposedness and illposedness of the Cauchy problem. Zbl 1106.35096
Gérard, Patrick
10
2006
Bilinear eigenfunction estimates and the nonlinear Schrödinger equation on surfaces. Zbl 1092.35099
Burq, N.; Gérard, P.; Tzvetkov, N.
85
2005
Multilinear eigenfunction estimates and global existence for the three dimensional nonlinear Schrödinger equations. Zbl 1116.35109
Burq, Nicolas; Gérard, Patrick; Tzvetkov, Nikolay
59
2005
Nonlinear Schrödinger equations on compact manifolds. Zbl 1076.35115
Gérard, P.
5
2005
Strichartz inequalities and the nonlinear Schrödinger equation on compact manifolds. Zbl 1067.58027
Burq, N.; Gérard, P.; Tzvetkov, N.
227
2004
On nonlinear Schrödinger equations in exterior domains. Zbl 1061.35126
Burq, N.; Gérard, P.; Tzvetkov, N.
47
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
A Landau-Zener formula for two-scaled Wigner measures. Zbl 1145.81368
Fermanian Kammerer, Clotilde; Gerard, Patrick
1
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 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.
26
2003
The Cauchy problem for the nonlinear Schrödinger equation on a compact manifold. Zbl 1362.35282
Burq, Nicolas; Gérard, Patrick; Tzvetkov, Nikolay
11
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.
64
2002
Semi-classical measures and eigenvalue crossings. (Mesures semi-classiques et croisement de modes.) Zbl 0996.35004
Fermanian-Kammerer, Clotilde; Gérard, Patrick
42
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
15
2001
The Schrödinger equation on a compact manifold: Strichartz estimates and applications. Zbl 1043.58019
Burq, Nicolas; Gérard, Patrick; Tzvetkov, Nikolay
6
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
49
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
225
1999
Description of the lack of compactness for the Sobolev imbedding. Zbl 0907.46027
Gérard, P.
129
1998
Generalized Strichartz estimates on the Heisenberg group. (Estimation de Strichartz généralisées sur le groupe de Heisenberg.) Zbl 1104.35303
Bahouri, Hajer; Gerard, Patrick; Xu, Chao-Jiang
1
1998
Homogenization limits and Wigner transforms. Zbl 0881.35099
Gérard, Patrick; Markowich, Peter A.; Mauser, Norbert J.; Poupaud, Frédéric
219
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
123
1997
Sharp Sobolev inequalities. (Inégalités de Sobolev précisées.) Zbl 1066.46501
Gerard, Patrick; Meyer, Yves; Oru, Frédérique
52
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
46
1996
A compactness result for generalized Radon transforms. Zbl 0864.44001
Gérard, Patrick; Golse, François; Wennberg, Bernt
2
1996
A microlocal version of concentration-compactness. Zbl 0868.35005
Gérard, Patrick
2
1996
Ergodic properties of eigenfunctions for the Dirichlet problem. Zbl 0788.35103
Gérard, Patrick; Leichtnam, Eric
109
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
17
1993
Diffraction of a wave at a corner. (Diffusion d’une onde par un coin.) Zbl 0779.35063
Gérard, Patrick; Lebeau, Gilles
13
1993
Averaging regularity results for PDEs under transversality assumptions. Zbl 0832.35020
Gérard, Patrick; Golse, François
17
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
10
1992
Microlocal defect measures. Zbl 0770.35001
Gérard, Patrick
231
1991
Pseudo-differential operators and the Nash-Moser theorem. (Opérateurs pseudo-différentiels et théorème de Nash-Moser.) Zbl 0791.47044
Alinhac, Serge; Gérard, Patrick
105
1991
Mesures semi-classiques et ondes de Bloch. (Semiclassical measures and Bloch waves). Zbl 0739.35096
Gérard, P.
49
1991
Moyennisation et régularité deux-microlocale. (Second microlocal averaging and regularity). Zbl 0725.35003
Gérard, Patrick
17
1990
Compacité par compensation et régularité 2-microlocale. (Compensated compactness and 2-microlocal regularity). Zbl 0707.35032
Gérard, P.
3
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.
9
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
2
1987
all top 5

Cited by 1,677 Authors

46 Gerard, Patrick
41 Tzvetkov, Nikolay
37 Burq, Nicolas
34 Cavalcanti, Marcelo Moreira
30 Fermanian-Kammerer, Clotilde
29 Carles, Rémi
26 Domingos Cavalcanti, Valéria Neves
24 Kenig, Carlos Eduardo
22 Duyckaerts, Thomas
20 Bahouri, Hajer
18 Bal, Guillaume
17 Gallagher, Isabelle
17 Jin, Shi
17 Visciglia, Nicola
16 Oh, Tadahiro
15 Markowich, Peter Alexander
15 Merle, Frank
15 Paul, Thierry
15 Ryzhik, Lenya
14 Antonić, Nenad
14 Gala, Sadek
14 Nakanishi, Kenji
14 Thomann, Laurent
14 Zuazua, Enrique
13 Macià, Fabricio
13 Panov, Evgeniy Yu.
12 Galkowski, Jeffrey
12 Laurent, Camille
12 Lawrie, Andrew G. W.
12 Léautaud, Matthieu
12 Miao, Changxing
11 Hani, Zaher
11 Israwi, Samer
11 Lebeau, Gilles
11 Mauser, Norbert Julius
11 Sun, Chenmin
11 Tataru, Daniel
11 Visan, Monica
10 Evnin, Oleg
10 Guo, Zihua
10 Ibrahim, Slim
10 Krieger, Joachim
10 Lasser, Caroline
10 Lazar, Martin
10 Masmoudi, Nader
10 Mitrovic, Darko
10 Perthame, Benoît
10 Ragusa, Maria Alessandra
10 Raphael, Pierre
10 Saut, Jean-Claude
10 Sogge, Christopher D.
10 Tacy, Melissa
10 Trélat, Emmanuel
9 Banica, Valeria
9 Grellier, Sandrine
9 Khorbatly, Bashar
9 Killip, Rowan
9 Pelinovsky, Dmitry Efimovich
9 Planchon, Fabrice
9 Schlag, Wilhelm
9 Secchi, Paolo
9 Sparber, Christof
9 Toth, John Andrew
8 Allaire, Grégoire
8 Aloui, Lassaad
8 Blair, Matthew D.
8 Erceg, Marko
8 Ervedoza, Sylvain
8 Gassot, Louise
8 Gonzalez Martinez, Victor Hugo
8 Gravejat, Philippe
8 Guardia, Marcel
8 Hassell, Andrew
8 Majdoub, Mohamed
8 Pausader, Benoît
8 Soler, Juan S.
8 Xu, Guixiang
8 Zelditch, Steven Morris
8 Zhu, Shihui
7 Alabau-Boussouira, Fatiha
7 Bao, Weizhu
7 Brzeźniak, Zdzisław
7 Christianson, Hans
7 Corrêa, Wellington José
7 Dehman, Belhassen
7 Dodson, Benjamin G.
7 Germain, Pierre
7 Jendrej, Jacek
7 Kwon, Soonsik
7 Lee, Sanghyuk
7 Lenzmann, Enno
7 Méhats, Florian
7 Morando, Alessandro
7 Panthee, Mahendra
7 Pierfelice, Vittoria
7 Pinaud, Olivier
7 Pocovnicu, Oana
7 Privat, Yannick
7 Pushnitski, Alexander B.
7 Ruzhansky, Michael V.
...and 1,577 more Authors
all top 5

Cited in 292 Serials

99 Journal of Differential Equations
74 Communications in Mathematical Physics
70 Journal of Functional Analysis
70 Communications in Partial Differential Equations
52 Archive for Rational Mechanics and Analysis
50 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire
43 Journal de Mathématiques Pures et Appliquées. Neuvième Série
36 Journal of Mathematical Analysis and Applications
34 Journal of Mathematical Physics
34 Comptes Rendus. Mathématique. Académie des Sciences, Paris
33 Transactions of the American Mathematical Society
32 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods
32 SIAM Journal on Mathematical Analysis
27 Nonlinearity
27 Analysis & PDE
24 Mathematische Annalen
24 Discrete and Continuous Dynamical Systems
22 Journal of the European Mathematical Society (JEMS)
21 Duke Mathematical Journal
21 Communications on Pure and Applied Analysis
20 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations
19 Communications on Pure and Applied Mathematics
19 Journal of Computational Physics
18 Proceedings of the American Mathematical Society
18 Séminaire Laurent Schwartz. EDP et Applications
17 Bulletin de la Société Mathématique de France
17 Inventiones Mathematicae
17 The Journal of Geometric Analysis
16 Advances in Mathematics
16 Journal of Hyperbolic Differential Equations
15 Annales de l’Institut Fourier
15 Pure and Applied Analysis
14 Mathematical Methods in the Applied Sciences
14 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série
14 Revista Matemática Iberoamericana
14 Journal of Dynamics and Differential Equations
14 Communications in Contemporary Mathematics
13 ZAMP. Zeitschrift für angewandte Mathematik und Physik
13 Mathematische Zeitschrift
13 Physica D
13 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences
11 Wave Motion
11 Asymptotic Analysis
11 Annales Henri Poincaré
11 Journal of Spectral Theory
10 Journal d’Analyse Mathématique
10 Journal of the American Mathematical Society
10 NoDEA. Nonlinear Differential Equations and Applications
10 Science China. Mathematics
9 Applicable Analysis
9 Annali di Matematica Pura ed Applicata. Serie Quarta
9 SIAM Journal on Control and Optimization
9 Calculus of Variations and Partial Differential Equations
9 Journal of Pseudo-Differential Operators and Applications
9 Annals of PDE
8 Mathematische Nachrichten
8 Geometric and Functional Analysis. GAFA
8 The Journal of Fourier Analysis and Applications
8 Journal of Evolution Equations
8 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis
7 Numerische Mathematik
7 Journal of Scientific Computing
7 Journal of Mathematical Sciences (New York)
7 Stochastic and Partial Differential Equations. Analysis and Computations
7 Evolution Equations and Control Theory
7 Journal de l’École Polytechnique – Mathématiques
6 Journal of Statistical Physics
6 Transport Theory and Statistical Physics
6 American Journal of Mathematics
6 Proceedings of the London Mathematical Society. Third Series
6 Quarterly of Applied Mathematics
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 Acta Mathematica Sinica. English Series
6 Nonlinear Analysis. Real World Applications
6 Multiscale Modeling & Simulation
6 Journal of Physics A: Mathematical and Theoretical
6 Annales Henri Lebesgue
5 Applied Mathematics and Optimization
5 Indiana University Mathematics Journal
5 Journal of the London Mathematical Society. Second Series
5 Memoirs of the American Mathematical Society
5 SIAM Journal on Applied Mathematics
5 Bulletin of the American Mathematical Society. New Series
5 Journal of Nonlinear Science
5 Discrete and Continuous Dynamical Systems. Series B
5 Journal of the Institute of Mathematics of Jussieu
5 Acta Numerica
5 Oberwolfach Reports
5 Discrete and Continuous Dynamical Systems. Series S
4 Letters in Mathematical Physics
4 Journal of Optimization Theory and Applications
4 Chinese Annals of Mathematics. Series B
4 Acta Applicandae Mathematicae
4 Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni
4 Potential Analysis
4 Applied and Computational Harmonic Analysis
4 St. Petersburg Mathematical Journal
4 Foundations of Computational Mathematics
...and 192 more Serials
all top 5

Cited in 53 Fields

1,597 Partial differential equations (35-XX)
263 Quantum theory (81-XX)
215 Global analysis, analysis on manifolds (58-XX)
215 Fluid mechanics (76-XX)
214 Dynamical systems and ergodic theory (37-XX)
139 Systems theory; control (93-XX)
128 Statistical mechanics, structure of matter (82-XX)
113 Operator theory (47-XX)
109 Harmonic analysis on Euclidean spaces (42-XX)
99 Functional analysis (46-XX)
90 Numerical analysis (65-XX)
73 Mechanics of deformable solids (74-XX)
65 Probability theory and stochastic processes (60-XX)
52 Calculus of variations and optimal control; optimization (49-XX)
52 Differential geometry (53-XX)
52 Optics, electromagnetic theory (78-XX)
35 Ordinary differential equations (34-XX)
32 Topological groups, Lie groups (22-XX)
29 Abstract harmonic analysis (43-XX)
24 Real functions (26-XX)
18 Relativity and gravitational theory (83-XX)
17 Number theory (11-XX)
16 Functions of a complex variable (30-XX)
12 Special functions (33-XX)
11 Measure and integration (28-XX)
11 Mechanics of particles and systems (70-XX)
11 Geophysics (86-XX)
10 Integral equations (45-XX)
9 General and overarching topics; collections (00-XX)
9 Integral transforms, operational calculus (44-XX)
9 Biology and other natural sciences (92-XX)
8 Potential theory (31-XX)
8 Approximations and expansions (41-XX)
7 Astronomy and astrophysics (85-XX)
6 Linear and multilinear algebra; matrix theory (15-XX)
5 Classical thermodynamics, heat transfer (80-XX)
5 Information and communication theory, circuits (94-XX)
4 Combinatorics (05-XX)
4 Several complex variables and analytic spaces (32-XX)
4 General topology (54-XX)
3 Group theory and generalizations (20-XX)
3 Difference and functional equations (39-XX)
3 Operations research, mathematical programming (90-XX)
2 History and biography (01-XX)
2 Algebraic geometry (14-XX)
2 Nonassociative rings and algebras (17-XX)
2 Sequences, series, summability (40-XX)
2 Geometry (51-XX)
2 Manifolds and cell complexes (57-XX)
2 Statistics (62-XX)
2 Game theory, economics, finance, and other social and behavioral sciences (91-XX)
1 Associative rings and algebras (16-XX)
1 Computer science (68-XX)

Citations by Year

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