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

TL;DR

This paper investigates the well-posedness of the KP-I equation on , establishing local well-posedness in certain Sobolev spaces for regularity levels above 1/2, thus improving previous results.

Contribution

It demonstrates that the KP-I equation is locally well-posed in $H^{s,0}$ for $s>1/2$, advancing the understanding of low regularity solutions.

Findings

Proves $C^0$ local well-posedness for $s>1/2$

Improves previous regularity thresholds

Enhances understanding of KP-I equation behavior

Abstract

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