Well-posedness of the Fifth Order Kadomtsev-Petviashvili I Equation in Anisotropic Sobolev Spaces with Nonnegative Indices

Details Well-posedness of the Fifth Order Kadomtsev-Petviashvili I Equation in Anisotropic Sobolev Spaces with Nonnegative Indices Well-posedness of the Fifth Order Kadomtsev-Petviashvili I Equation in Anisotropic Sobolev Spaces with Nonnegative Indices

2008-01-14

arxiv.org/abs/0801.2129v1

Mathematics

Analysis of PDEs

17pages

Scientific paper

In this paper we establish the local and global well-posedness of the real
valued fifth order Kadomstev-Petviashvili I equation in the anisotropic Sobolev
spaces with nonnegative indices. In particular, our local well-posedness
improves Saut-Tzvetkov's one and our global well-posedness gives an affirmative
answer to Saut-Tzvetkov's $L^2$-data conjecture.

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