Boundary Partial $$C^{1, \alpha }$$ C 1 , α -Regularity for Stationary Shear Thickening Flows in 3D

Abstract

In this paper, we prove boundary partial regularity result for weak solutions to systems describing stationary shear thickening flows in 3D smooth domains. We show that the weak solution is in $$C^{1,\,\alpha }$$ with any $$\alpha \in (0,\,1)$$ in a neighbourhood of almost all boundary points. In particular, we show that for the regularity criterion at the boundary, only the normal derivative is of importance.