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 $u_{tt}-u_{xx}+u_{xxxx}-(|u{|}^{2}u{)}_{xx}=0$ on the real line is globally well-posed in $H^s(\mathbb{R})$ provided $2/3<s<1$.

21 pages, to appear, Journal of the London Mathematical Society. Many suggestions of the referee implemented

Cited by in corpus (1)

• The Cauchy problem for the nonlinear viscous Boussinesq equation in the $L^q$ framework