Differential and Integral Equations
- Differential Integral Equations
- Volume 18, Number 10 (2005), 1111-1146.
Local well posedness for modified Kadomstev-Petviashvili equations
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 , and also on previous work of the authors, . 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 , 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.
Differential Integral Equations, Volume 18, Number 10 (2005), 1111-1146.
First available in Project Euclid: 21 December 2012
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Kenig, C. E.; Ziesler, S. N. Local well posedness for modified Kadomstev-Petviashvili equations. Differential Integral Equations 18 (2005), no. 10, 1111--1146. https://projecteuclid.org/euclid.die/1356060108