三维Brinkman-Forchheimer方程强解的全局吸引子的存在性

研究了三维有界区域上Brinkman-Forchheimer方程■-γ△u+au+b|u|u+c|u|βu+▽p=f强解的存在唯一性及强解的全局吸引子的存在性.首先证明了当5/2≤β≤4及初始值u0∈H01(Ω)时强解的存在唯一性.接着对强解进行了一系列一致估计,基于这些一致估计,借助半群理论证明了方程的强解分别在H11(Ω)和H2(Ω)空间中具有全局吸引子,并证明了H01(Ω)中的全局吸引子实际上便是H2(Ω)中的全局吸引子.

The Existence of Global Attractors for the Strong Solutions of Three-dimensional Brinkman-Forchheimer Equations

In this paper, we discuss the uniqueness of strong solutions and the existence of global attractors for the three-dimensional autonomous Brinkman-Forchheimer equations ■-γ△u+au+b|u|u+c|u|βu+▽p=f. Firstly, we prove the uniqueness of strong solutions when 5/2≤β≤4 and initial data u0∈H01(Ω).Then we give a series of uniformly estimates on the solutions. Based on these estimates, applying semigroup theory, we show that the strong solutions of the equations has global attractors in H11(Ω) and H2(Ω). And we prove the global attractor in H01(Ω) is actually the global attractor in H2(Ω).