Asymptotic behavior for the singularly perturbed damped Boussinesq equation

This work is focused on the long-time behavior of solutions to the singularly perturbed damped Boussinesq equation in a 3D case where ε > 0 is small enough. Without any growth restrictions on the nonlinearity f(u), we establish in an appropriate bounded phase space a finite dimensional global attractor as well as an exponential attractor of optimal regularity. The key step is the estimate of the difference between the solutions of the damped Boussinesq equation and the corresponding pseudo-parabolic equation.Copyright © 2014 John Wiley & Sons, Ltd.