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

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

An inverse source problem for convective Brinkman-Forchheimer equations with the final overdetermination

“…So, we restrict ourselves to periodic domains in this work, and the equality (7) plays a crucial role in obtaining the well-posedness of solutions of the inverse problem (1)- (5). Recently, the authors in [45] addressed the above regularity problem for Dirichlet's boundary conditions and the well-posedness of such kinds of inverse problems for CBF equations in bounded domains will be a future work.…”