Global existence and long-time behavior of the initial-boundary value problem for the dissipative Boussinesq equation

We investigate the initial-boundary value problem of n-dimensional (n≥1) dissipative Boussinesq equation. The global existence, uniqueness and stability of the strong solutions are obtained by means of the Faedo-Galërkin method. We discuss the long-time behavior of the strong solutions so as to prove the existence of global compact attractor and exponential attractor.