Abstract: We considered the longtime dynamical behavior of solutions of Boussinesq equations with  memory. Firstly, the original equation was transformed into a dynamical system by introducing a new variable. Secondly, the compactness of corresponding solutions semigroups associated with problem was proved by using the technique of operator decomposition and the compactness theorem on historical spaces. Finally, the exponential attractor of the memorytype Boussinesq equation was obtained by combining the existence of the exponential attractor, and the finite fractal dimension of the global attractor of the problem was obtained.

Key words: Boussinesq equations, linear memory, exponential attractor, operator decomposition