Attractors for nonautonomous 2D Navier-Stokes equations with less regular symbols

We introduce a new class of functions satisfying normal Condition (C*), denoted by , which are translation bounded but not translation compact — in particular, which are more general than normal functions (see [S.S. Lu, H.Q. Wu, C.K. Zhong, Attractors for nonautonomous 2D Navier-Stokes equations with normal external forces, Discrete Contin. Dyn. Syst., 13 (2005) 701-719] for the definition), denoted by . Furthermore, we prove the existence of uniform attractors for 2D Navier-Stokes equations with external forces belonging to in .