Asymptotic regularity and attractors for slightly compressible Brinkman-Forcheimer equations

Abstract

Slightly compressible Brinkman-Forchheimer equations in a bounded 3D domain with Dirichlet boundary conditions are considered. These equations model fluids motion in porous media. The dissipativity of these equations in higher order energy spaces is obtained and regularity and smoothing properties of the solutions are studied. In addition, the existence of a global and an exponential attractors for these equations in a natural phase space is verified.

References in corpus (2)

• A note on a strongly damped wave equation with fast growing nonlinearities
• Infinite energy solutions for weakly damped quintic wave equations in ${\mathbb{R}}^3$