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.