In this article we consider the Boussinesq system supplemented with some dissipation terms. These equations model the propagation of a water wave in shallow water. We prove the existence of a global smooth attractor for the corresponding dynamical system.
M. Abounouh. A. Atlas. O. Goubet. "Large-time behavior of solutions to a dissipative Boussinesq system." Differential Integral Equations 20 (7) 755 - 768, 2007. https://doi.org/10.57262/die/1356039408