Global well-posedness for KdV in Sobolev Spaces of negative index

TL;DR

This paper proves that the KdV equation is globally well-posed for initial data in Sobolev spaces with negative index, extending the understanding of solutions for rough initial conditions.

Contribution

It establishes global well-posedness for the KdV equation in Sobolev spaces with negative regularity, which was previously unresolved.

Findings

Global well-posedness for H^s with s > -3/10

Extension of solution theory to rough initial data

Advancement in understanding low-regularity solutions

Abstract

The initial value problem for the Korteweg-deVries equation on the line is shown to be globally well-posed for rough data. In particular, we show global well-posedness for initial data in H^s({\mathbb{R}), -3/10<s.