Le problème de Cauchy pour des EDP semi-linéaires périodiques en variables d'espace
Séminaire Bourbaki (1994-1995)
- Volume: 37, page 163-187
- ISSN: 0303-1179
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topGinibre, Jean. "Le problème de Cauchy pour des EDP semi-linéaires périodiques en variables d'espace." Séminaire Bourbaki 37 (1994-1995): 163-187. <http://eudml.org/doc/110197>.
@article{Ginibre1994-1995,
author = {Ginibre, Jean},
journal = {Séminaire Bourbaki},
keywords = {nonlinear Schrödinger equation; generalized KdV equation; Kadomtsev-Petviashvili equation; Cauchy problem},
language = {fre},
pages = {163-187},
publisher = {Société Mathématique de France},
title = {Le problème de Cauchy pour des EDP semi-linéaires périodiques en variables d'espace},
url = {http://eudml.org/doc/110197},
volume = {37},
year = {1994-1995},
}
TY - JOUR
AU - Ginibre, Jean
TI - Le problème de Cauchy pour des EDP semi-linéaires périodiques en variables d'espace
JO - Séminaire Bourbaki
PY - 1994-1995
PB - Société Mathématique de France
VL - 37
SP - 163
EP - 187
LA - fre
KW - nonlinear Schrödinger equation; generalized KdV equation; Kadomtsev-Petviashvili equation; Cauchy problem
UR - http://eudml.org/doc/110197
ER -
References
top- [B1] J. Bourgain - Fourier restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations I, Schrödinger equations, Geom. and Funct. Anal.3 (1993), 107-156. Zbl0787.35097MR1209299
- [B2] J. Bourgain - Id. II, The KdV equations, Ibid.3 (1993), 209-262. Zbl0787.35098MR1215780
- [B3] J. Bourgain - Exponential sums and nonlinear Schrödinger equations, Ibid.3 (1993), 157-178. Zbl0787.35096MR1209300
- [B4] J. Bourgain - On the Cauchy problem for the Kadomtsev-Petviashvili equation, Ibid.3 (1993), 315-341. Zbl0787.35086MR1223434
- [B5] J. Bourgain - On the Cauchy problem for periodic KdV type equations, prétirage IHES (1994). MR1364878
- [B6] J. Bourgain - Periodic nonlinear Schrödinger equation and invariant measures, Commun. Math. Phys.166 (1994), 1-26. Zbl0822.35126MR1309539
- [B7] J. Bourgain - Invariant measures for the 2D-defocusing nonlinear Schrö- dinger equation, prétirage IHES (1994).
- [B8] J. Bourgain - On the long time behaviour of nonlinear Hamiltonian equations, prétirage IHES (1994).
- [C] T. Cazenave - An introduction to nonlinear Schrödinger equations, Text. Met. Mat.22, Inst. Mat., Rio de Janeiro (1989).
- [CW] T. Cazenave and F. Weissler - The Cauchy problem for the nonlinear Schrödinger equation in Hs, Nonlinear Anal. TMA14 (1990), 807-836. Zbl0706.35127MR1055532
- [GV] J. Ginibre and G. Velo - Smoothing properties and retarded estimates for some dispersive evolution equations, Commun. Math. Phys.144 (1992), 163- 188. Zbl0762.35008MR1151250
- [G] E. Grosswald - Representation of integers as sums of squares, Springer, Berlin (1985). Zbl0574.10045MR803155
- [K] T. Kato - On nonlinear Schrödinger equations, Ann. IHP (Phys. Théor.)46 (1987), 113-129. Zbl0632.35038MR877998
- [KPV1] C. Kenig, G. Ponce and L. Vega - Oscillatory integrals and regularity of dispersive equations, Indiana U. Math. J.40 (1991), 33-69. Zbl0738.35022MR1101221
- [KPV2] C. Kenig, G. Ponce and L. Vega - Well posedness and scattering results for the generalized Korteweg-de Vries equation via the contraction principle, Comm. Pure Appl. Math.46 (1993), 527-620. Zbl0808.35128MR1211741
- [KPV3] C. Kenig, G. Ponce and L. Vega - The Cauchy problem for the Korteweg-de Vries equation in Sobolev spaces of negative indices, Duke Math. J.71 (1993), 1-21. Zbl0787.35090MR1230283
- [KPV4] C. Kenig, G. Ponce and L. Vega - A bilinear estimate with applications to the KdV equation, prétirage (1994).
- [KM] S. Klainerman and M. Machedon - Smoothing estimates for null forms and applications, prétirage (1994). MR1301438
- [S] R. Strichartz - Restrictions of Fourier transforms to quadratic surfaces and decay of solutions of wave equations, Duke Math. J.44 (1977), 705-714. Zbl0372.35001MR512086
- [Y] K. Yajima - Existence of solutions for Schrödinger evolution equations, Commun. Math. Phys.110 (1987), 415-426. Zbl0638.35036MR891945
- [Z] A. Zygmund - On Fourier coefficients and transforms of functions of two variables, Studia Math.50 (1974), 189-201. Zbl0278.42005MR387950
Citations in EuDML Documents
top- Nikolay Tzvetkov, Invariant measures for the defocusing Nonlinear Schrödinger equation
- Nikolay Tzvetkov, Bilinear estimates related to the KP equations
- Nicolas Burq, Patrick Gérard, Nikolay Tzvetkov, Estimées multilinéaires de projecteurs spectraux et équations de Schrodinger non linéaires
- Tohru Ozawa, Kimitoshi Tsutaya, Yoshio Tsutsumi, On the coupled system of nonlinear wave equations with different propagation speeds
- Nikolay Tzvetkov, On the local well-posedness of the KP equations
- Camille Laurent, Global controllability and stabilization for the nonlinear Schrödinger equation on an interval
- Nicolas Burq, Patrick Gérard, Nikolay Tzvetkov, Multilinear eigenfunction estimates and global existence for the three dimensional nonlinear Schrödinger equations
- Patrick Gérard, Vittoria Pierfelice, Nonlinear Schrödinger equation on four-dimensional compact manifolds
- Sebastian Herr, Energy Critical nonlinear Schrödinger equations in the presence of periodic geodesics
- Nicolas Burq, Patrick Gérard, Nikolay Tzvetkov, Inégalités de Sogge bilinéaires et équation de Schrödinger non linéaire
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