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2005 Local well posedness for modified Kadomstev-Petviashvili equations
C. E. Kenig, S. N. Ziesler
Differential Integral Equations 18(10): 1111-1146 (2005).

Abstract

In this paper we consider the Kadomstev-Petivashvili equation and also the modified Kadomstev-Petviashvili equation, with nonlinearity $\partial_x(u^3).$ We improve on previous results of Iório and Nunes [5], and also on previous work of the authors, [13]. For the modified $(KP-II)$ equation we give optimal (up to endpoint) maximal function type estimates for the solution of the associated linear initial-value problem. These estimates enable us to obtain a local well-posedness result via the contraction mapping principle. For modified $(KP-I)$ we use methods developed by Kenig in [9], which use an energy estimate together with Strichartz estimates and "interpolation inequalities." We give some counterexamples to well posedness via the contraction mapping principle, for both the Kadomstev-Petviashvili equation and the modified equation.

Citation

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C. E. Kenig. S. N. Ziesler. "Local well posedness for modified Kadomstev-Petviashvili equations." Differential Integral Equations 18 (10) 1111 - 1146, 2005.

Information

Published: 2005
First available in Project Euclid: 21 December 2012

zbMATH: 1212.35419
MathSciNet: MR2162626

Subjects:
Primary: 35Q53
Secondary: 35B30

Rights: Copyright © 2005 Khayyam Publishing, Inc.

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Vol.18 • No. 10 • 2005
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