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

Abstract

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].