Gain of Regularity for the KP-I Equation

Julie Levandosky, Mauricio Sepulveda (DIM), Octavio Vera
Arxiv ID: 0708.2102Last updated: 1/24/2023
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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