Gain of Regularity for the KP-I Equation

Details Gain of Regularity for the KP-I Equation Gain of Regularity for the KP-I Equation

2007-08-15

arxiv.org/abs/0708.2102v1

Journal of Differential Equations 245, 3 (2008) 762-808

Mathematics

Analysis of PDEs

Scientific paper

10.1016/j.jde.2008.01.016

In this paper we study the smoothness properties of solutions to the KP-I equation. We show that the equation's dispersive nature leads to a gain in regularity for the solution. In particular, if the initial data $\phi$ possesses certain regularity and sufficient decay as $x \to \infty$, then the solution $u(t)$ will be smoother than $\phi$ for $0 < t \leq T$ where $T$ is the existence time of the solution.

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