Inertial manifolds of incompressible, nonlinear bipolar viscous fluids

Abstract

The existence of an inertial manifold is established for the nonlinear system of equations describing the motion of a bipolar incompressible viscous fluid. In this paper we consider only the case of a spatially periodic velocity field. Existence of an inertial manifold for the model complements earlier work on the existence of compact global attractors for bipolar viscous fluids and serves to further highlight the differences between the bipolar model and the usual model based on the linear Stokes constitutive relation.