Uniform attractor for a two-dimensional nonautonomous incompressible non-Newtonian fluid

Abstract

We discuss the long time behavior of solutions for a two-dimensional (2D) nonautonomous incompressible non-Newtonian fluid in 2D bounded domains. When the external force g 0 ( x , t ) is translation compact (tr.c.) in L loc 2 ( R ; H ) , we obtain the existence and reveal the structure of the uniform attractor for the processes associated to the fluid by constructing skew product flow on the extended phase space. When ‖ g 0 ‖ L b 2 is properly small, we establish that there exists a unique bounded asymptotically stable solution to the fluid.