A Uniform Attractor for a Non-Autonomous Generalized Navier-Stokes Equation

Abstract

A global existence and uniqueness result of a weak solution for a generalized non-autonomous Navier-Stokes equation is given, independently of the dimension $n\ge 2$ of the space. Furthermore, the family of processes associated to the equation is shown to-possess a weak uniform attractor with respect to a large class of non-autonomous forcing terms.