Well-posedness of the Fifth Order Kadomtsev-Petviashvili I Equation in Anisotropic Sobolev Spaces with Nonnegative Indices

TL;DR

This paper proves local and global well-posedness for the fifth order Kadomtsev-Petviashvili I equation in anisotropic Sobolev spaces, improving previous results and confirming a conjecture about $L^2$ data.

Contribution

It establishes the well-posedness of the equation in broader spaces and confirms the $L^2$-data conjecture, advancing understanding of the equation's mathematical properties.

Findings

Improved local well-posedness results.

Established global well-posedness in $L^2$ spaces.

Confirmed Saut-Tzvetkov's $L^2$-data conjecture.

Abstract

In this paper we establish the local and global well-posedness of the real valued fifth order Kadomstev-Petviashvili I equation in the anisotropic Sobolev spaces with nonnegative indices. In particular, our local well-posedness improves Saut-Tzvetkov's one and our global well-posedness gives an affirmative answer to Saut-Tzvetkov's $L^2$-data conjecture.