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

Abstract 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–Galerkin method. We discuss the long-time behavior of the strong solutions so as to prove the existence of global compact attractor and exponential attractor.