On the local regularity of the KP-I equation in anisotropic Sobolev space

Zihua Guo, Lizhong Peng, Baoxiang Wang

We prove that the KP-I initial-value problem \begin{eqnarray*} \begin{cases} \partial_tu+\partial_x^3u-\partial_x^{-1}\partial_y^2u+\partial_x(u^2/2)=0 {on}{\R}^2_{x,y}\times {\R}_…