On KP-II Type Equations on Cylinders
GrüNrock, Axel ; Panthee, Mahendra ; Drumond Silva, Jorge
Annales de l'I.H.P. Analyse non linéaire, Tome 26 (2009), p. 2335-2358 / Harvested from Numdam
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@article{AIHPC_2009__26_6_2335_0,
     author = {Gr\"uNrock, Axel and Panthee, Mahendra and Drumond Silva, Jorge},
     title = {On KP-II Type Equations on Cylinders},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     volume = {26},
     year = {2009},
     pages = {2335-2358},
     doi = {10.1016/j.anihpc.2009.04.002},
     mrnumber = {2569897},
     zbl = {pre05649875},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPC_2009__26_6_2335_0}
}

GrüNrock, Axel; Panthee, Mahendra; Drumond Silva, Jorge. On KP-II Type Equations on Cylinders. Annales de l'I.H.P. Analyse non linéaire, Tome 26 (2009) pp. 2335-2358. doi : 10.1016/j.anihpc.2009.04.002. http://gdmltest.u-ga.fr/item/AIHPC_2009__26_6_2335_0/

[1] Bourgain J., On the Cauchy Problem for the Kadomtsev-Petviashvili Equation, Geom. Funct. Anal. 3 (4) (1993) 315-341. | MR 1223434 | Zbl 0787.35086

[2] Bourgain J., Periodic Korteweg De Vries Equation With Measures as Initial Data, Selecta Math. (N.S.) 3 (1997) 115-159. | MR 1466164 | Zbl 0891.35138

[3] Ben-Artzi M., Saut J.-C., Uniform Decay Estimates for a Class of Oscillatory Integrals and Applications, Differential Integral Equations 12 (2) (1999) 137-145. | MR 1672730 | Zbl 1016.35006

[4] Ginibre J., Tsutsumi Y., Velo G., On the Cauchy Problem for the Zakharov System, J. Funct. Anal. 151 (1997) 384-436. | MR 1491547 | Zbl 0894.35108

[5] A. Grünrock, New applications of the Fourier restriction norm method to wellposedness problems for nonlinear evolution equations, thesis, Universität Wuppertal, 2002.

[6] Hadac M., Well-Posedness for the Kadomtsev-Petviashvili Equation (KPII) and Generalisations, Trans. Amer. Math. Soc. 360 (2008) 6555-6572. | MR 2434299 | Zbl 1157.35094

[7] M. Hadac, On the local well-posedness of the Kadomtsev-Petviashvili II equation, thesis, Universität Dortmund, 2007.

[8] Hadac M., Herr S., Koch H., Well-Posedness and Scattering for the KP-II Equation in a Critical Space, Ann. Inst. H. Poincaré Anal. Non Linéaire 26 (3) (2009) 917-941. | Numdam | MR 2526409 | Zbl 1169.35372

[9] Isaza P., Lopez J., Mejia J., The Cauchy Problem for the Kadomtsev-Petviashvili (KPII) Equation in Three Space Dimensions, Comm. Partial Differential Equations 32 (2007) 611-641. | MR 2334825 | Zbl 1123.35058

[10] Isaza P., Mejia J., Local and Global Cauchy Problems for the Kadomtsev-Petviashvili (KPII) Equation in Sobolev Spaces of Negative Indices, Comm. Partial Differential Equations 26 (2001) 1027-1054. | MR 1843294 | Zbl 0993.35080

[11] Kenig C. E., Ponce G., Vega L., Oscillatory Integrals and Regularity of Dispersive Equations, Indiana Univ. Math. J. 40 (1) (1991) 33-69. | MR 1101221 | Zbl 0738.35022

[12] Kenig C. E., Ponce G., Vega L., A Bilinear Estimate With Applications to the KdV Equation, J. Amer. Math. Soc. 9 (2) (1996) 573-603. | MR 1329387 | Zbl 0848.35114

[13] Saut J.-C., Remarks on the Generalized Kadomtsev-Petviashvili Equations, Indiana Univ. Math. J. 42 (3) (1993) 1011-1026. | MR 1254130 | Zbl 0814.35119

[14] Saut J.-C., Tzvetkov N., The Cauchy Problem for Higher-Order KP Equations, J. Differential Equations 153 (1999) 196-222. | MR 1682263 | Zbl 0927.35098

[15] Saut J.-C., Tzvetkov N., The Cauchy Problem for the Fifth Order KP Equations, J. Math. Pures Appl. 79 (4) (2000) 307-338. | MR 1753060 | Zbl 0961.35137

[16] Saut J.-C., Tzvetkov N., On Periodic KP-I Type Equations, Comm. Math. Phys. 221 (2001) 451-476. | MR 1852048 | Zbl 0984.35143

[17] Takaoka H., Tzvetkov N., On the Local Regularity of the Kadomtsev-Petviashvili-II Equation, Int. Math. Res. Not. IMRN (2) (2001) 77-114. | MR 1810481 | Zbl 0977.35126

[18] H. Takaoka, N. Tzvetkov, On the local well-posedness of the KP-II equation on T×R, unpublished manuscript.

[19] Tzvetkov N., Remark on the Local Ill-Posedness for KdV Equation, C. R. Acad. Sci. Paris Sér. I 329 (1999) 1043-1047. | MR 1735881 | Zbl 0941.35097