一类非自治Brinkman-Forchheimer方程的一致吸引子

Uniform Attractors for a Non-Autonomous Brinkman-Forchheimer Equation

中文关键词:  Galerkin逼近  一致吸引子  非自治Brinkman-Forchheimer方程.

英文关键词:Galerkin approximation  uniform attractor  non-autonomous Brinkman-Forchheimer equation.

中文摘要:

      文中研究了三维非自治Brinkman-Forchheimer方程. 利用Galerkin逼近方法，给出了非自治Brinkman-Forchheimer方程弱解的存在性和唯一性. 接着讨论了弱解的渐进行为, $(H,H)$一致吸引子和$(H,V)$一致吸引子的存在性和结构. 然后证明了$L^2$一致吸引子实际上便是$H^1$一致吸引子.

英文摘要:

      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.