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 $r^{-3}{\int }_{B_r^{+}}|u(x){|}^{3}dx$ or $r^{-2}{\int }_{B_r^{+}}|\nabla u(x){|}^{2}dx$ 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 \cite{DS}.

22 pages. Compared with the last version, we add the partial regularity of 6D steady MHD equations

References in corpus (3)

• Boundary partial regularity for the high dimensional Navier-Stokes equations
• Partial Regularity of solutions to the Four-Dimensional Navier-Stokes Equations
• On the interior regularity criterion and the number of singular points to the Navier-Stokes equations