Global Regularity of Shear Thickening Stokes System with Dirichlet Boundary Condition on Non-smooth Domains

We study a shear thickening Stokes system in a non-smooth domain. Our purpose is to derive a Calderon-Zygmund type estimate of the gradient of a solution under a small BMO non-linearity and a sufficient flatness on the boundary of the domain. In the process, we overcome not only the lack of Lipschitz regularity for the corresponding limiting problem, but also the fact that the associated structure depends only on the symmetric part of the gradient for the desired global estimate, which is new even in the literature of the elliptic system on a non-smooth domain.