Unconditional well-posedness for the Kawahara equation

TL;DR

This paper proves the unconditional well-posedness of the Kawahara equation on the real line for initial data in L^2, using an infinite iteration scheme of normal form reductions.

Contribution

It establishes the first unconditional well-posedness result for the Kawahara equation in L^2 using novel infinite iteration techniques.

Findings

Unconditional well-posedness in L^2 for the Kawahara equation.

Application of infinite normal form reductions.

Method applicable to similar dispersive equations.

Abstract

This article is concerned with the unconditional well-posedness for the Kawahara equation on the real line and shows that this holds true for initial data in $L^2(\mathbb{R})$. This is achieved by applying an infinite iteration scheme of normal form reductions.