On the well-posedness of the KP-I equation

Abstract

We revisit the local well-posedness for the KP-I equation. We obtain unconditional local well-posedness in $H^{s,0}({\mathbb{R}}^2)$ for $s>3/4$ and unconditional global well-posedness in the energy space. We also prove the global existence of perturbations with finite energy of non decaying smooth global solutions.

We improved the manuscript. In particular, we corrected an error in the definition 2.2 of the admissible pairs for the Strichartz estimates