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1 November 2002 Well-posedness and ill-posedness results for the Kadomtsev-Petviashvili-I equation
L. Molinet, J.-C. Saut, N. Tzvetkov
Duke Math. J. 115(2): 353-384 (1 November 2002). DOI: 10.1215/S0012-7094-02-11525-7

Abstract

The main results of this paper are concerned with the "bad" behavior of the KP-I equation with respect to a Picard iteration scheme applied to the associated integral equation, for data in usual or anisotropic Sobolev spaces. This leads to some kind of ill-posedness of the corresponding Cauchy problem: the flow map cannot be of class $C\sp 2$ in any Sobolev space.

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L. Molinet. J.-C. Saut. N. Tzvetkov. "Well-posedness and ill-posedness results for the Kadomtsev-Petviashvili-I equation." Duke Math. J. 115 (2) 353 - 384, 1 November 2002. https://doi.org/10.1215/S0012-7094-02-11525-7

Information

Published: 1 November 2002
First available in Project Euclid: 26 May 2004

zbMATH: 1033.35103
MathSciNet: MR1944575
Digital Object Identifier: 10.1215/S0012-7094-02-11525-7

Subjects:
Primary: 35Q53
Secondary: 35B30 , 35R25

Rights: Copyright © 2002 Duke University Press

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Vol.115 • No. 2 • 1 November 2002
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