On the local and global well-posedness theory for the KP-I equation
Annales de l'I.H.P. Analyse non linéaire, Tome 21 (2004) no. 6, pp. 827-838.
@article{AIHPC_2004__21_6_827_0,
     author = {Kenig, Carlos E.},
     title = {On the local and global well-posedness theory for the {KP-I} equation},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {827--838},
     publisher = {Elsevier},
     volume = {21},
     number = {6},
     year = {2004},
     doi = {10.1016/j.anihpc.2003.12.002},
     mrnumber = {2097033},
     zbl = {1072.35162},
     language = {en},
     url = {http://archive.numdam.org/articles/10.1016/j.anihpc.2003.12.002/}
}
TY  - JOUR
AU  - Kenig, Carlos E.
TI  - On the local and global well-posedness theory for the KP-I equation
JO  - Annales de l'I.H.P. Analyse non linéaire
PY  - 2004
SP  - 827
EP  - 838
VL  - 21
IS  - 6
PB  - Elsevier
UR  - http://archive.numdam.org/articles/10.1016/j.anihpc.2003.12.002/
DO  - 10.1016/j.anihpc.2003.12.002
LA  - en
ID  - AIHPC_2004__21_6_827_0
ER  - 
%0 Journal Article
%A Kenig, Carlos E.
%T On the local and global well-posedness theory for the KP-I equation
%J Annales de l'I.H.P. Analyse non linéaire
%D 2004
%P 827-838
%V 21
%N 6
%I Elsevier
%U http://archive.numdam.org/articles/10.1016/j.anihpc.2003.12.002/
%R 10.1016/j.anihpc.2003.12.002
%G en
%F AIHPC_2004__21_6_827_0
Kenig, Carlos E. On the local and global well-posedness theory for the KP-I equation. Annales de l'I.H.P. Analyse non linéaire, Tome 21 (2004) no. 6, pp. 827-838. doi : 10.1016/j.anihpc.2003.12.002. http://archive.numdam.org/articles/10.1016/j.anihpc.2003.12.002/

[1] Bona J.L., Smith R., The initial value problem for the Korteweg-de Vries equation, Philos. Trans. Roy. Soc. London Ser. A 278 (1975) 555-601. | MR | Zbl

[2] Bourgain J., On the Cauchy problem for the Kadomstev-Petviashvili equation, Geom. Funct. Anal. 3 (1993) 315-341. | MR | Zbl

[3] Coifman R., Meyer Y., Au delà des operateurs pseudodifferéntiels, Astérisque 57 (1978). | Numdam | MR | Zbl

[4] Colliander J., Kenig C., Staffilani G., Small solutions for the Kadomstev-Petviashvili I equation, Mosc. Math. J. 1 (4) (2001) 491-520. | MR | Zbl

[5] J. Colliander, C. Kenig, G. Staffilani, Low regularity solutions for the Kadomstev-Petviashvili I equation, Geom. Funct. Anal., submitted for publication. | MR | Zbl

[6] J. Colliander, C. Kenig, G. Staffilani, Corrections to: On solutions for the Kadomstev-Petviashvili I equation, Mosc. Math. J., submitted for publication. | MR | Zbl

[7] Iorio R.J., Nunes W.V.L., On equations of KP-type, Proc. Roy. Soc. Edinburgh Sect. A 128 (1998) 725-743. | MR | Zbl

[8] Journé J.L., Two problems of Calderón-Zygmund theory on product-spaces, Ann. Inst. Fourier Grenoble 38 (1) (1988) 111-132. | Numdam | MR | Zbl

[9] Kato T., Ponce G., Commutator estimates and the Euler and Navier-Stokes equations, Comm. Pure Appl. Math. 41 (1988) 891-907. | MR | Zbl

[10] C. Kenig, K. Koenig, On the local well-posedness of the Benjamin-Ono and modified Benjamin-Ono equations, MRL, submitted for publication. | MR | Zbl

[11] Kenig C., Ponce G., Vega L., Well-posedness and scattering results for the generalized Korteweg-de Vries equation via the contraction principle, Comm. Pure Appl. Math. 46 (1993) 527-620. | MR | Zbl

[12] Koch H., Tzvetkov N., Local well-posedness of the Benjamin-Ono equation in H s R, IMRN 26 (2003) 1449-1464. | MR | Zbl

[13] Molinet L., Saut J.-C., Tzvetkov N., Well-posedness and ill-posedness results for the Kadomstev-Petviashvili I equation, Duke Math. J. 115 (2) (2002) 353-384. | MR | Zbl

[14] Molinet L., Saut J.-C., Tzvetkov N., Global well-posedness for the KP-I equation, Math. Annalen 324 (2002) 255-275. | MR | Zbl

[15] L. Molinet, J.-C. Saut, N. Tzvetkov, Correction: Global well-posedness for the KP-I equation, Math. Annalen, submitted for publication. | Zbl

[16] C. Muscalu, J. Pipher, T. Tao, C. Thiele, Bi-parameter paraproducts, preprint. | MR

[17] Saut J.-C., Remarks on the generalized Kadomstev-Petviashvili equations, Indiana Univ. Math. J. 42 (1993) 1011-1026. | MR | Zbl

[18] Takaoka H., Time local well-posedness for the Kadomstev-Petviashvili II equation, Harmonic Anal. Nonlin. PDE 1102 (1999) 1-8. | MR | Zbl

[19] Tzvetkov N., Global low regularity solutions for Kadomstev-Petviashvili equation, Differential Integral Equations 13 (2000) 1289-1320. | MR | Zbl

[20] Takaoka H., Tzvetkov N., On the local regularity of Kadomstev-Petviashvili-II equation, IMRN 8 (2001) 77-114. | MR | Zbl

Cité par Sources :