Attractors for nonautonomous nonhomogeneous Navier - Stokes equations

Abstract

In this paper our aim is to derive an upper bound on the dimension of the attractor of the family of processes associated to the Navier - Stokes equations with nonhomogeneous boundary conditions depending on time. We consider two-dimensional flows with prescribed quasiperiodic (in time) tangential velocity at the boundary, and obtain an upper bound which is polynomial with respect to the viscosity.