On the well-posedness of the KP-I equation

Zihua Guo; Luc Molinet

On the well-posedness of the KP-I equation

Analysis of PDEs 2026-04-02 v2

Authors: Zihua Guo , Luc Molinet

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.

Keywords

KP-I equation well-posedness Sobolev spaces energy space global existence unconditional local well-posedness perturbations

Cite

@article{arxiv.2404.12364,
  title  = {On the well-posedness of the KP-I equation},
  author = {Zihua Guo and Luc Molinet},
  journal= {arXiv preprint arXiv:2404.12364},
  year   = {2026}
}

Comments

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

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