Global rough solutions to the cubic nonlinear Boussinesq equation

TL;DR

This paper establishes global well-posedness for the cubic nonlinear Boussinesq equation in a specific Sobolev space range, advancing understanding of its solution behavior.

Contribution

It proves global well-posedness of the IVP for the cubic defocusing nonlinear Boussinesq equation in Sobolev spaces with 2/3<s<1, a new result in the field.

Findings

Global well-posedness in H^s for 2/3<s<1

Extension of solution existence to lower regularity spaces

Advances understanding of nonlinear dispersive PDEs

Abstract

We prove that the initial value problem (IVP) for the cubic defocusing nonlinear Boussinesq equation $u_{tt}-u_{xx}+u_{xxxx}-(|u|^2u)_{xx}=0$ on the real line is globally well-posed in $H^{s}(\R)$ provided $2/3<s<1$.