Le problème de Cauchy pour des EDP semi-linéaires périodiques en variables d'espace

Jean Ginibre

Séminaire Bourbaki (1994-1995)

  • Volume: 37, page 163-187
  • ISSN: 0303-1179

How to cite

top

Ginibre, 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
  1. [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
  2. [B2] J. Bourgain - Id. II, The KdV equations, Ibid.3 (1993), 209-262. Zbl0787.35098MR1215780
  3. [B3] J. Bourgain - Exponential sums and nonlinear Schrödinger equations, Ibid.3 (1993), 157-178. Zbl0787.35096MR1209300
  4. [B4] J. Bourgain - On the Cauchy problem for the Kadomtsev-Petviashvili equation, Ibid.3 (1993), 315-341. Zbl0787.35086MR1223434
  5. [B5] J. Bourgain - On the Cauchy problem for periodic KdV type equations, prétirage IHES (1994). MR1364878
  6. [B6] J. Bourgain - Periodic nonlinear Schrödinger equation and invariant measures, Commun. Math. Phys.166 (1994), 1-26. Zbl0822.35126MR1309539
  7. [B7] J. Bourgain - Invariant measures for the 2D-defocusing nonlinear Schrö- dinger equation, prétirage IHES (1994). 
  8. [B8] J. Bourgain - On the long time behaviour of nonlinear Hamiltonian equations, prétirage IHES (1994). 
  9. [C] T. Cazenave - An introduction to nonlinear Schrödinger equations, Text. Met. Mat.22, Inst. Mat., Rio de Janeiro (1989). 
  10. [CW] T. Cazenave and F. Weissler - The Cauchy problem for the nonlinear Schrödinger equation in Hs, Nonlinear Anal. TMA14 (1990), 807-836. Zbl0706.35127MR1055532
  11. [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
  12. [G] E. Grosswald - Representation of integers as sums of squares, Springer, Berlin (1985). Zbl0574.10045MR803155
  13. [K] T. Kato - On nonlinear Schrödinger equations, Ann. IHP (Phys. Théor.)46 (1987), 113-129. Zbl0632.35038MR877998
  14. [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
  15. [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
  16. [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
  17. [KPV4] C. Kenig, G. Ponce and L. Vega - A bilinear estimate with applications to the KdV equation, prétirage (1994). 
  18. [KM] S. Klainerman and M. Machedon - Smoothing estimates for null forms and applications, prétirage (1994). MR1301438
  19. [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
  20. [Y] K. Yajima - Existence of solutions for Schrödinger evolution equations, Commun. Math. Phys.110 (1987), 415-426. Zbl0638.35036MR891945
  21. [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
  1. Nikolay Tzvetkov, Invariant measures for the defocusing Nonlinear Schrödinger equation
  2. Nikolay Tzvetkov, Bilinear estimates related to the KP equations
  3. Nicolas Burq, Patrick Gérard, Nikolay Tzvetkov, Estimées multilinéaires de projecteurs spectraux et équations de Schrodinger non linéaires
  4. Camille Laurent, Global controllability and stabilization for the nonlinear Schrödinger equation on an interval
  5. Tohru Ozawa, Kimitoshi Tsutaya, Yoshio Tsutsumi, On the coupled system of nonlinear wave equations with different propagation speeds
  6. Nikolay Tzvetkov, On the local well-posedness of the KP equations
  7. Sebastian Herr, Energy Critical nonlinear Schrödinger equations in the presence of periodic geodesics
  8. Nicolas Burq, Patrick Gérard, Nikolay Tzvetkov, Inégalités de Sogge bilinéaires et équation de Schrödinger non linéaire
  9. Patrick Gérard, Sur le caractère bien posé des équations de Schrödinger non linéaires
  10. Nicolas Burq, Patrick Gérard, Nikolay Tzvetkov, Multilinear eigenfunction estimates and global existence for the three dimensional nonlinear Schrödinger equations

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.