Partial regularity of solution to generalized Navier-Stokes problem

Abstract

In the presented work, we study the regularity of solutions to the generalized Navier-Stokes problem up to a C2 boundary in dimensions two and three. The point of our generalization is an assumption that a deviatoric part of a stress tensor depends on a shear rate and on a pressure. We focus on estimates of the Hausdorff measure of a singular set which is defined as a complement of a set where a solution is Hölder continuous. We use so-called indirect approach to show partial regularity, for dimension 2 we get even an empty set of singular points.