Global rough solutions to the cubic nonlinear Boussinesq equation

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 $2/3<s<1$.