Mathematics

CLC number: O175.29

Existence of Global Attractor for a 3D Brinkman-Forchheimer Equfation in Some Poincaré Unbounded Domains

College of Science, Xi'an University of Science and Technology, Xi'an 710054, Shaanxi, China

Received: 6 January 2023

Abstract

In this paper, we study the existence of global attractor of a class of three-dimensional Brinkman-Forchheimer equation in some unbounded domains which satisfies Poincaré inequality. We use the tail estimation method to establish the asymptotic compactness of the solution operator and then prove the existence of the global attractor in $(H_{\mathrm{0}}^{\mathrm{1}}{(\mathrm{\Omega }))}^{\mathrm{3}}$.