Electronic Journal of Differential Equations, Vol. 2024 (2024), No. 47, pp. 1-35.

Title: Global gradient estimates for shear thinning-type Stokes system on  non-smooth domains

Author: Namkyeong Cho (POSTECH, South Korea)

Abstract: 
This article presents global L^q estimates for the weak solution of 
the steady p-Stokes equations, which describe the motion of shear-thinning 
flow under the nonslip boundary condition. We focus on non-smooth domains 
whose boundaries extend beyond the Lipschitz category, with coefficients 
belonging to the BMO (Bounded Mean Oscillation) space having a sufficiently 
small BMO semi-norm.

Submitted May 8, 2024. Published August 26, 2024.
Math Subject Classifications: 35Q35, 35J25, 35J92.
Key Words: Stokes system; Reifenberg flat; symmetric gradient; non-Newtonian fluid.