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

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 g0(x,t) is translation compact (tr.c.) in Lloc2(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 ‖g0‖Lb2 is properly small, we establish that there exists a unique bounded asymptotically stable solution to the fluid.