On Global Solutions for the Cauchy Problem of a Boussinesq-Type Equation

Abstract

We will give conditions which will guarantee the existence of global weak solutions of the Boussinesq-type equation with power-type nonlinearity $\gamma {|u|}^p$ and supercritical initial energy. By defining new functionals and using potential well method, we readdressed the initial value problem of the Boussinesq-type equation for the supercritical initial energy case.