Uniform Attractors for a Non-Autonomous Brinkman-Forchheimer Equation

Abstract:

      This paper is concerned with the three-dimensional non-autonomous Brinkman-Forchheimer equation. By Galerkin approximation method, we give the existence and uniqueness of weak solutions for non-autonomous Brinkman-Forchheimer equation. And we investigate the asymptotic behavior of the weak solution, the existence and structures of the $(H,H)$-uniform attractor and $(H,V)$-uniform attractor. Then we prove that an $L^2$-uniform attractor is actually an $H^1$-uniform attractor.