The non-autonomous Navier-Stokes-Brinkman-Forchheimer equation with Dirichlet boundary conditions: dissipativity, regularity, and attractors

TL;DR

This paper investigates the 3D Navier-Stokes-Brinkman-Forchheimer equations with Dirichlet boundary conditions, focusing on solution regularity, dissipativity, and the existence of uniform attractors under non-autonomous forces.

Contribution

It provides a comprehensive analysis of regularity, dissipativity, and attractors for these equations with non-autonomous external forces in bounded domains.

Findings

Establishment of dissipativity in higher energy spaces

Proof of existence of uniform attractors

Analysis of solution regularity under given conditions

Abstract

We give a comprehensive study of the 3D Navier-Stokes-Brinkman-Forchheimer equations in a bounded domain endowed with the Dirichlet boundary conditions and non-autonomous external forces. This study includes the questions related with the regularity of weak solutions, their dissipativity in higher energy spaces and the existence of the corresponding uniform attractors