Global attractors of two-dimensional micropolar fluid flows in some unbounded domains

Abstract

This paper is concerned with the existence and regularity of the global attractors of micropolar fluid flows in two-dimensional unbounded domains, in which the Poincaré inequality holds true. Based on an asymptotic compactness argument, a L 2 global attractor is shown to exist if the stationary external vector field is in H −1. Moreover, if the external vector field is in L 2, then the L 2 global attractor becomes an H 1 global attractor.