Uniform attractors for nonautonomous incompressible non-Newtonian fluid with locally uniform integrable external forces

Abstract

This paper discusses the long time behavior of solutions for a two-dimensional (2D) nonautonomous incompressible non-Newtonian fluid in 2D bounded domains. When the external force g0(x,t) is locally uniform integrable (see Definition 1.1) in Lloc2(R;H), the authors obtain the existence and structure of uniform attractors in space V for the family of processes associated with the fluid. Moreover, when ∥g0∥Lb2 is properly small, they provide some interesting corollaries.