Duke Mathematical Journal

Well-posedness and ill-posedness results for the Kadomtsev-Petviashvili-I equation

L. Molinet, J.-C. Saut, and N. Tzvetkov

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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.

Article information

Source
Duke Math. J., Volume 115, Number 2 (2002), 353-384.

Dates
First available in Project Euclid: 26 May 2004

Permanent link to this document
https://projecteuclid.org/euclid.dmj/1085598146

Digital Object Identifier
doi:10.1215/S0012-7094-02-11525-7

Mathematical Reviews number (MathSciNet)
MR1944575

Zentralblatt MATH identifier
1033.35103

Subjects
Primary: 35Q53: KdV-like equations (Korteweg-de Vries) [See also 37K10]
Secondary: 35B30: Dependence of solutions on initial and boundary data, parameters [See also 37Cxx] 35R25: Improperly posed problems

Citation

Molinet, L.; Saut, J.-C.; Tzvetkov, N. Well-posedness and ill-posedness results for the Kadomtsev-Petviashvili-I equation. Duke Math. J. 115 (2002), no. 2, 353--384. doi:10.1215/S0012-7094-02-11525-7. https://projecteuclid.org/euclid.dmj/1085598146


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References

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