## Global solution for the Kadomtsev-Petviashvili equation (KPII) in anisotropic Sobolev spaces of negative indices.(English)Zbl 1037.35068

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 $$s>-1/14$$. 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.

### MSC:

 35Q53 KdV equations (Korteweg-de Vries equations) 35B30 Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs
Full Text: