Attractors for the 3D autonomous and nonautonomous Brinkman-Forchheimer equations

作者：Zhang, Lingrui^*; Su, Keqin; Wen, Shenglan

来源：Boundary Value Problems, 2016, 2016(1): 17.

DOI：10.1186/s13661-016-0519-5

• Brinkman-Forchheimer equation
• symbol
• processes
• uniform attractor

We consider the large-time behavior such as the existence of attractors for the 3D autonomous and nonautonomous Brinkman-Forchheimer equations. By means of the decomposition method we overcome the difficulties for the existence of absorbing sets and asymptotical compactness of the semigroup generated by a global solution to prove the attractors for the autonomous Brinkman-Forchheimer equation. Under suitable assumptions on the external force sigma(t, x) and initial data u(tau)(x), we prove the existence of a uniform attractor for a 3D nonautonomous Brinkman-Forchheimer equation. Moreover, we apply the theory of weak continuity and weak convergence method to establish the asymptotical compactness of the processes.

• 出版日期2016-1-18
• 单位中国人民解放军信息工程大学; 河南师范大学; 河南农业大学