Partial regularity of a certain class of non-Newtonian fluids

We study the partial regularity of weak solution to a certain class of non-Newtonian fluids (1.1)-(1.3), the existence of weak solution to such system had been provided by D. Pierre and H. Norbert in [40]. In particular, we prove that the regularity point in QT is an open set with full measure, and we obtain a general criterion for a weak solution to be regular in the neighborhood of a given point. In this paper we confined ourselves to considered the case p=2 and space dimension d=2.