@article{SEDP_2000-2001____A15_0, author = {Tzvetkov, Nikolay}, title = {On the local well-posedness of the {KP} equations}, journal = {S\'eminaire \'Equations aux d\'eriv\'ees partielles (Polytechnique) dit aussi "S\'eminaire Goulaouic-Schwartz"}, note = {talk:15}, pages = {1--11}, publisher = {Centre de math\'ematiques Laurent Schwartz, \'Ecole polytechnique}, year = {2000-2001}, zbl = {02124165}, language = {en}, url = {http://www.numdam.org/item/SEDP_2000-2001____A15_0/} }
TY - JOUR AU - Tzvetkov, Nikolay TI - On the local well-posedness of the KP equations JO - Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" N1 - talk:15 PY - 2000-2001 SP - 1 EP - 11 PB - Centre de mathématiques Laurent Schwartz, École polytechnique UR - http://www.numdam.org/item/SEDP_2000-2001____A15_0/ LA - en ID - SEDP_2000-2001____A15_0 ER -
%0 Journal Article %A Tzvetkov, Nikolay %T On the local well-posedness of the KP equations %J Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" %Z talk:15 %D 2000-2001 %P 1-11 %I Centre de mathématiques Laurent Schwartz, École polytechnique %U http://www.numdam.org/item/SEDP_2000-2001____A15_0/ %G en %F SEDP_2000-2001____A15_0
Tzvetkov, Nikolay. On the local well-posedness of the KP equations. Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" (2000-2001), Exposé no. 15, 11 p. http://www.numdam.org/item/SEDP_2000-2001____A15_0/
[1] B. Birnir, C. Kenig, G. Ponce, N. Svanstedt, L. Vega, On the ill-posedness of the IVP for the generalized Korteweg-de Vries and nonlinear Schrödinger equations, Annales I.H.P., Analyse non linéaire 13 (1996), 529-535. | Numdam | MR | Zbl
[2] B. Birnir, G. Ponce, N. Svanstedt, The local ill-posedness of the modified KdV equation, J. London Math. Soc. 53 (1996), 551-559. | MR | Zbl
[3] J. Bourgain, Fourier transform restriction phenomena for certain lattice subsets and application to nonlinear evolution equations I. Schrödinger equations, GAFA 3 (1993), 107–156, II. The KdV equation, GAFA 3 (1993), 209–262. | MR | Zbl
[4] J. Bourgain, On the Cauchy problem for the Kadomtsev-Petviashvili equation, GAFA 3 (1993), 315-341. | MR | Zbl
[5] J. Bourgain, Periodic KdV equation with measures as initial data, Sel. Math. New Ser. 3 (1997) 115-159. | MR | Zbl
[6] J. Bourgain, Refinements of Strichartz’ inequality and applications to 2D-NLS with critical nonlinearity, IMRN 5 (1998), 253-283. | Zbl
[7] J. Ginibre, Le problème de Cauchy pour des EDP semi-linéaires périodiques en variables d’espace (d’après Bourgain), Séminaire Bourbaki n. 796, Astérisque 237 (1996), 163-187. | Numdam | Zbl
[8] P. Isaza, J. Mejia, Problemas de Cauchy local y global para la ecuacion de Kadomtsev-Petviashvili (KP-II) en espacios de Sobolev con indices negativos, Preprint.
[9] C. E. Kenig, G. Ponce, L. Vega, Well-posedness and scattering results for the generalized KdV equations via the contraction principle, Comm. Pure Appl. Math. 46 (1993), 527-620. | MR | Zbl
[10] C. E. Kenig, G. Ponce, L. Vega, A bilinear estimate with applications to the KdV equations, J. AMS, 9 (1996), 573-603. | MR | Zbl
[11] C. E. Kenig, G. Ponce, L. Vega, On the ill-posedness of some canonical dispersive equations, Preprint 2000. | MR
[12] L. Molinet, F. Ribaud, The global Cauchy problem in Bourgain’s type spaces for a dissipative semilinear equation, Preprint 2000. | MR
[13] L. Molinet, J.C. Saut, N. Tzvetkov, Well-posedness and ill-posedness for the Kadomtsev-Petviashvili-I equation, Preprint 2001. | MR
[14] L. Molinet, J.C. Saut, N. Tzvetkov, Ill-posedness issues for the Benjamin-Ono and related equations, Preprint 2001. | MR
[15] F. Ribaud, A. Youssfi, Well-posedness and ill-posedness for a semilinear heat equation, Preprint 2001.
[16] J. C. Saut, Remarks on the generalized Kadomtsev-Petviashvili equations, Indiana Univ. Math. J., 42 (1993), 1017-1029. | MR | Zbl
[17] J.C. Saut, N. Tzvetkov, The Cauchy problem for higher order KP equations, J. Diff. Eq. 153 (1999), 196-222. | MR | Zbl
[18] J.C. Saut, N. Tzvetkov, The Cauchy problem for the fifth order KP equations, J. Math. Pures Appl. 79 (2000), 307-338. | MR | Zbl
[19] J. C. Saut, N. Tzvetkov, On periodic KP-I type equations , Preprint 2000. | MR | Zbl
[20] H. Takaoka, Global well-posedness for the Kadomtsev-Petviashvili II equation, Discrete Contin. Dynam. Systems, 6 (2000), 483–499. | MR | Zbl
[21] H. Takaoka, N. Tzvetkov, On the local regularity of Kadomtsev-Petviashvili-II equation, IMRN 8 (2001), 77-114. | MR | Zbl
[22] T. Tao, Multilinear weighted convolution of functions, and applications to non-linear dispersive equations, Amer. J. Math. (to appear). | MR | Zbl
[23] N. Tzvetkov, Remark on the local ill-posedness for KdV equation, C. R. Acad. Sci. Paris, 329 (1999), 1043-1047. | MR | Zbl
[24] N. Tzvetkov, Global low regularity solutions for Kadomtsev-Petviashvili equation, Diff. Int. Eq. 13 (2000), 1289-1320. | MR | Zbl
[25] V. Zakharov, Weakly nonlinear waves on the surface of an ideal finite depth fluid, Amer. Math. Soc. Transl. 182 (1998), 167-197. | MR | Zbl
[26] V. Zakharov, E. Schulman, Degenerative dispersion laws, motion invariants and kinetic equations, Physica 1D (1980), 192-202. | MR