A global nonlinear evolution problem for generalized Newtonian fluids : local initial regularity of the strong solution

Abstract

We consider the strong solution of an initial boundary value problem for a system of evolution equations describing the flow of a generalized Newtonian fluid of power law type. For a rather large scale of growth rates we prove local initial regularity results such as higher integrability of the pressure function or the existence of the second spatial derivatives of the velocity field.