Geodesic
Global solution for the Kadomtsev-Petviashvili equation (KPII) in anisotropic Sobolev spaces of negative indices
Electronic journal of differential equations, Tome 2003 (2003)
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__a83,
     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},
     year = {2003},
     volume = {2003},
     zbl = {1037.35068},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2003__2003__a83/}
}
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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__a83/