Geodesic
Global solution for the Kadomtsev-Petviashvili equation (KPII) in anisotropic Sobolev spaces of negative indices
Electronic Journal of Differential Equations, Tome 2003 (2003).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: It is proved that the Cauchy problem for the Kadomtsev-Petviashvili equation (KPII) is globally well-posed for initial data in anisotropic Sobolev spaces $H^{s0}(\mathbb{R}^2)$ with $s greater than -1/14$. The extension of a local solution to a solution in an arbitrary interval is carried out by means of an almost conservation property of the $H^{s0}$ norm of the solution.
Classification : 35Q53, 37K05
Keywords: nonlinear dispersive equations, global solutions, almost conservation laws 
@article{EJDE_2003__2003__a183,
     author = {Isaza J., Pedro and Mej{\'\i}a L., Jorge},
     title = {Global solution for the {Kadomtsev-Petviashvili} equation {(KPII)} in anisotropic {Sobolev} spaces of negative indices},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2003},
     year = {2003},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2003__2003__a183/}
}
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Isaza J., Pedro; Mejía L., Jorge. Global solution for the Kadomtsev-Petviashvili equation (KPII) in anisotropic Sobolev spaces of negative indices. Electronic Journal of Differential Equations, Tome 2003 (2003). http://geodesic.mathdoc.fr/item/EJDE_2003__2003__a183/