Remark on the low regularity well-posedness of the KP-I equation

Abstract

We study the Cauchy problem to the KP-I equation posed on ${\mathbb{R}}^2$. We prove that it is $C^0$ locally well-posed in $H^{s,0}(\mathbb{R}\times \mathbb{R})$ for $s>1/2$, which improves the previous results in \cite{GPW,GMo}.