Low regularity well-posedness for KP-I equations: the dispersion-generalized case. (English) Zbl 1522.35449
Local-in-time well-posedness of the Cauchy problem for the Kadomtsev-Petviashvili I equation in \(\mathbb{R}^2\) is studied in the framework of anisotropic Sobolev spaces. The data-to-solution mapping is shown to be nonanalytic (neither \(C^2\)). Methods used include Strichartz inequalities as well as a nonlinear version of Loomis-Whitney inequality for convolutions.
Reviewer: Piotr Biler (Wrocław)
MSC:
35Q53 | KdV equations (Korteweg-de Vries equations) |
35R11 | Fractional partial differential equations |
42B37 | Harmonic analysis and PDEs |
35B65 | Smoothness and regularity of solutions to PDEs |
35A01 | Existence problems for PDEs: global existence, local existence, non-existence |
35A02 | Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness |
Keywords:
Kadomtsev-Petviashvili I equation; generalized dispersion; well-posedness; anisotropic Sobolev spacesReferences:
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