Boundary regularity criteria for the 6D steady Navier-Stokes and MHD equations

It is shown in this paper that suitable weak solutions to the 6D steady incompressible Navier-Stokes and MHD equations are Hölder continuous near boundary provided that either r−3∫Br+|u(x)|3dx or r−2∫Br+|∇u(x)|2dx is sufficiently small, which implies that the 2D Hausdorff measure of the set of singular points near the boundary is zero. This generalizes recent interior regularity results by Dong-Strain [5].