On the Cauchy problem for the Kadomtsev-Petviashvili equation
type: Item
instance of: scholarly article
title: On the Cauchy problem for the Kadomtsev-Petviashvili equation
zbMATH Open document ID: 0787.35086
DOI: 10.1007/BF01896259
published in: Geometric and Functional Analysis. GAFA
publication date: 1994-05-19T00:00:00Z
full work available at URL: https://eudml.org/doc/58131
review text: The author gives a global result for the Cauchy problem of the Kadomtsev- Petviashvili equation. The solution is globally well-posed for initial data in \(L^ 2(\mathbb{R}^ 2/\mathbb{Z}^ 2)\). The result is obtained on extending a local result (obtained by applying a Picard fixed point argument) to a global one with the help of the \(L^ 2\)-conservation law. The method is analogous to the one used for the Schrödinger and Korteweg-de Vries equations, and it is based on an analysis of multiple Fourier series.
Mathematics Subject Classification ID: 35Q53
Mathematics Subject Classification ID: 42B10
Mathematics Subject Classification ID: 31B10
zbMATH DE Number: 464906
zbMATH Keywords: wellposedness
zbMATH Keywords: Fourier analysis
zbMATH Keywords: periodic solution
zbMATH Keywords: Picard theorem
zbMATH Keywords: local solution
zbMATH Keywords: global solution
zbMATH Keywords: Cauchy problem
zbMATH Keywords: Kadomtsev-Petviashvili equation
zbMATH Keywords: multiple Fourier series
author: Jean Bourgain
reviewed by: L. Vázquez
MaRDI profile type: Publication
cites work: Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. I: Schrödinger equations
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description: scientific article; zbMATH DE number 464906