Boundary Regularity for the Steady Generalized Newtonian Flow with Shear Thickening Viscosity

Abstract

We work on the boundary regularity for weak solutions to the stationary Navier–Stokes type equations with shear dependent viscosity, which shows the Hölder continuity. For the proof, we first approximate the equations by adding the Laplacian to the viscosity term, then estimate the tangential derivatives. Later, using weighted embedding techniques we estimate the normal derivative.