Existence of weak solutions to a class of non-Newtonian flows

Abstract

We show that there exist weak solutions to a class of non-Newtonian flows for the periodic domain. Galerkin approximation, an W-1,W-r+2 compactness theorem, and Kern type inequalities are main ingredients for the proof of the existence of weak solutions. Moreover, we estimate the Hausdorff dimension of the set of singular times for the weak solutions.