Boundary Regularity Criteria for the 6D Steady Navier-Stokes and MHD Equations

Jitao Liu; Wendong Wang

Boundary Regularity Criteria for the 6D Steady Navier-Stokes and MHD Equations

Analysis of PDEs 2015-04-28 v2

Authors: Jitao Liu , Wendong Wang

Abstract

It is shown in this paper that suitable weak solutions to the 6D steady incompressible Navier-Stokes and MHD equations are H\"older continuous near boundary provided that either $r^{-3}\int_{B_r^+}|u(x)|^3dx$ or $r^{-2}\int_{B_r^+}|\nabla u(x)|^2dx$ 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 \cite{DS}.

Keywords

navier-stokes equations mhd equations boundary regularity weak solutions h\"older continuity hausdorff measure singular points

Cite

@article{arxiv.1309.3158,
  title  = {Boundary Regularity Criteria for the 6D Steady Navier-Stokes and MHD Equations},
  author = {Jitao Liu and Wendong Wang},
  journal= {arXiv preprint arXiv:1309.3158},
  year   = {2015}
}

Comments

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

Boundary Regularity Criteria for the 6D Steady Navier-Stokes and MHD Equations

Abstract

Keywords

Cite

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