Global rough solutions to the critical generalized KdV equation

TL;DR

This paper establishes global well-posedness for the critical generalized KdV equation in Sobolev spaces with regularity above 3/5, advancing understanding of its solutions' behavior.

Contribution

It proves global well-posedness for the critical generalized KdV equation in Sobolev spaces with minimal regularity s>3/5, extending previous results.

Findings

Global well-posedness for s>3/5

Solutions exist and are unique for all time

Regularity threshold improved

Abstract

We prove that the initial value problem (IVP) for the critical generalized KdV equation $u_{t}+u_{xxx}+(u^5)_{x}=0$ on the real line is globally well-posed in $H^{s}(\R)$ provided $s>3/5$.