Gain of Regularity for the KP-I Equation

Abstract

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 $\varphi$ possesses certain regularity and sufficient decay as $x\to \infty$, then the solution $u(t)$ will be smoother than $\varphi$ for $0<t\le T$ where $T$ is the existence time of the solution.

References in corpus (1)

• Global well-posedness for the KP-I equation on the background of a non localized solution

Cited by in corpus (2)

• Smoothing properties for the higher order nonlinear Schrödinger equation with constant coefficients
• Singularity for Solutions of Linearized KdV Equations