@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},
pages = {2335--2358},
year = {2009},
publisher = {Elsevier},
volume = {26},
number = {6},
doi = {10.1016/j.anihpc.2009.04.002},
mrnumber = {2569897},
language = {en},
url = {https://www.numdam.org/articles/10.1016/j.anihpc.2009.04.002/}
}
TY - JOUR AU - GrüNrock, Axel AU - Panthee, Mahendra AU - Drumond Silva, Jorge TI - On KP-II Type Equations on Cylinders JO - Annales de l'I.H.P. Analyse non linéaire PY - 2009 SP - 2335 EP - 2358 VL - 26 IS - 6 PB - Elsevier UR - https://www.numdam.org/articles/10.1016/j.anihpc.2009.04.002/ DO - 10.1016/j.anihpc.2009.04.002 LA - en ID - AIHPC_2009__26_6_2335_0 ER -
%0 Journal Article %A GrüNrock, Axel %A Panthee, Mahendra %A Drumond Silva, Jorge %T On KP-II Type Equations on Cylinders %J Annales de l'I.H.P. Analyse non linéaire %D 2009 %P 2335-2358 %V 26 %N 6 %I Elsevier %U https://www.numdam.org/articles/10.1016/j.anihpc.2009.04.002/ %R 10.1016/j.anihpc.2009.04.002 %G en %F 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) no. 6, pp. 2335-2358. doi: 10.1016/j.anihpc.2009.04.002
[1] , On the Cauchy Problem for the Kadomtsev-Petviashvili Equation, Geom. Funct. Anal. 3 (4) (1993) 315-341. | Zbl | MR
[2] , Periodic Korteweg De Vries Equation With Measures as Initial Data, Selecta Math. (N.S.) 3 (1997) 115-159. | Zbl | MR
[3] , , Uniform Decay Estimates for a Class of Oscillatory Integrals and Applications, Differential Integral Equations 12 (2) (1999) 137-145. | Zbl | MR
[4] , , , On the Cauchy Problem for the Zakharov System, J. Funct. Anal. 151 (1997) 384-436. | Zbl | MR
[5] A. Grünrock, New applications of the Fourier restriction norm method to wellposedness problems for nonlinear evolution equations, thesis, Universität Wuppertal, 2002.
[6] , Well-Posedness for the Kadomtsev-Petviashvili Equation (KPII) and Generalisations, Trans. Amer. Math. Soc. 360 (2008) 6555-6572. | Zbl | MR
[7] M. Hadac, On the local well-posedness of the Kadomtsev-Petviashvili II equation, thesis, Universität Dortmund, 2007.
[8] , , , 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. | Zbl | MR | Numdam
[9] , , , The Cauchy Problem for the Kadomtsev-Petviashvili (KPII) Equation in Three Space Dimensions, Comm. Partial Differential Equations 32 (2007) 611-641. | Zbl | MR
[10] , , 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. | Zbl | MR
[11] , , , Oscillatory Integrals and Regularity of Dispersive Equations, Indiana Univ. Math. J. 40 (1) (1991) 33-69. | Zbl | MR
[12] , , , A Bilinear Estimate With Applications to the KdV Equation, J. Amer. Math. Soc. 9 (2) (1996) 573-603. | Zbl | MR
[13] , Remarks on the Generalized Kadomtsev-Petviashvili Equations, Indiana Univ. Math. J. 42 (3) (1993) 1011-1026. | Zbl | MR
[14] , , The Cauchy Problem for Higher-Order KP Equations, J. Differential Equations 153 (1999) 196-222. | Zbl | MR
[15] , , The Cauchy Problem for the Fifth Order KP Equations, J. Math. Pures Appl. 79 (4) (2000) 307-338. | Zbl | MR
[16] , , On Periodic KP-I Type Equations, Comm. Math. Phys. 221 (2001) 451-476. | Zbl | MR
[17] , , On the Local Regularity of the Kadomtsev-Petviashvili-II Equation, Int. Math. Res. Not. IMRN (2) (2001) 77-114. | Zbl | MR
[18] H. Takaoka, N. Tzvetkov, On the local well-posedness of the KP-II equation on , unpublished manuscript.
[19] , Remark on the Local Ill-Posedness for KdV Equation, C. R. Acad. Sci. Paris Sér. I 329 (1999) 1043-1047. | Zbl | MR
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