Attractors for nonautonomous 2d Navier-Stokes equations with normal external forces

Theexistence and structure of uniform attractors in V is proved fornonautonomous 2D Navier-stokes equations on bounded domain with anew class of external forces, termed normal inLl o c²( R; H) (see Definition 3.1), which aretranslation bounded but not translation compact inLl o c²( R; H). To this end, some abstractresults are established. First, a characterization on theexistence of uniform attractor for a family of processes ispresented by the concept of measure of noncompactness as well as amethod to verify it. Then, the structure of the uniform attractoris obtained by constructing skew product flow on the extendedphase space with weak topology. Finally, the uniform attractor ofa process is identified with that of a family of processes withsymbols in the closure of the translation family of the originalsymbol in a Banach space with weak topology.