Gromov–Hausdorff stability of global attractors for 3D Brinkman–Forchheimer equations

Abstract

In this paper, using the Gromov–Hausdorff distances between two global attractors (which may be in disjoint phase spaces) and two semi‐dynamical systems introduced by Lee et al. (2020), we consider the continuous dependence of the global attractors and the stability of the semi‐dynamical systems on global attractors induced by the Brinkman–Forchheimer equation under variation of the domain. The results of this paper improve on previous results, which can compare any two systems in different phase spaces without the process of “pull‐backing” the perturbed systems to the original domain.