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

We introduce a new class of functions satisfying normal Condition (C*), denoted by Lnc∗2(R;X), 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 Ln2(R;X). Furthermore, we prove the existence of uniform attractors for 2D Navier–Stokes equations with external forces belonging to Lnc∗2(R;L2(Ω)) in H01.