Global existence and time-decay rates of solutions to the generalized Boussinesq equation with weak damping

Abstract

In this paper, we study the initial value problem for the generalized Boussineq equation with weak damping. The existence and time-decay rates of global solutions and its derivatives are established for all space dimensions d ≥ 1, provided that the norm of the initial data is suitably small. The negative Sobolev norms of the initial data in low frequency are shown to be preserved along time evolution and enhance the decay rates of global solutions. The proof is based on the energy method and flexible interpolation trick without investigating the corresponding linear equation.