Global Existence and Decay of Solutions for the Generalized Bad Boussinesq Equation

Abstract

In this paper, we consider the global existence of solutions for the Cauchy problem of the generalized sixth order bad Boussinesq equation. Moreover, we show that the supremum norm of the solution decays algebraically to zero as (1 + t)(-(1/7)) when t approaches to infinity, provided the initial data are sufficiently small and regular.