Boundary Regularity for the Steady Generalized Newtonian Flow with Shear Thickening Viscosity - Wolf, Jörg; Bae, Hyeong Ohk (Journal of Mathematical Fluid Mechanics, 2022)
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.
Keywords: Boundary regularity; Generalized Newtonian; Holder continuity; Holder regularity; Laplacians; Navier Stokes; Shear thickening; Shear-dependent viscosity; Shear-thickening fluids; Weak solution; Boundary regularity; Hölder regularity; Non-Newtonian fluid; Shear thickening fluid