Regularity of Flows of a Non-Newtonian Fluid in Two Dimensions subject to Dirichlet Boundary Conditions

Abstrakt

We study regularity of a planar flow of a generalized Newtonian fluid under the Dirichlet boundary condition. We prove that the unique weak solution of the problem has a Hoelder continuous gradient provided the growth of the stress tensor is of order p-1 for a certain p in [2,4).