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

Abstract

We introduce a new class of functions satisfying normal Condition (C*), denoted by L n c ∗ 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 L n 2 ( R ; X ) . Furthermore, we prove the existence of uniform attractors for 2D Navier–Stokes equations with external forces belonging to L n c ∗ 2 ( R ; L 2 ( Ω ) ) in H 0 1 .