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Well-posedness for the Kadomtsev-Petviashvili II equation. (English) Zbl 0994.35108

Summary: We study the well-posedness for the Cauchy problem of the KP II equation. We prove the local well-posedness in the anisotropic Sobolev spaces \(H_{x,y}^{-1/4 +\varepsilon,0}\) and in the anisotropic homogeneous Sobolev spaces \(H_{x,y}^{-1/2+4 \varepsilon,0} \cap H_{x,y}^{-1/2+ \varepsilon,0}\). The first result is an improvement of the result in \(L^2\) obtained by J. Bourgain [Geom. Funct. Anal. 3, Mo. 4, 315-341 (1993; Zbl 0787.35086)].

MSC:

35Q53 KdV equations (Korteweg-de Vries equations)
35A07 Local existence and uniqueness theorems (PDE) (MSC2000)
35B35 Stability in context of PDEs
35B60 Continuation and prolongation of solutions to PDEs

Citations:

Zbl 0787.35086
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