Asymptotic regularity and attractors for slightly compressible Brinkman-Forcheimer equations

TL;DR

This paper investigates the mathematical properties of slightly compressible Brinkman-Forchheimer equations, demonstrating dissipativity, regularity, and the existence of global and exponential attractors in 3D porous media flow models.

Contribution

It establishes dissipativity, regularity, and attractor existence for these equations, advancing understanding of their long-term behavior in porous media.

Findings

Proves dissipativity in higher order energy spaces

Shows regularity and smoothing of solutions

Establishes existence of global and exponential attractors

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.