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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
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