Boundary regularity criteria for suitable weak solutions of the magnetohydrodynamic equations

2012/08/24 by Kyungkeun Kang, Kang, Kyungkeun, Jae‐Myoung Kim +2 · 1 citation
Mathematics · #35Q35 #76D03 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Nonlinear Partial Differential Equations #math.AP #msc:35Q35 #msc:76D03

paper · pdf · doi:10.48550/arxiv.1208.4928

22 pages

arxiv created 2012/08/24 · openalex publication_date 2012/08/24 · arxiv updated 2012/08/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present some new regularity criteria for suitable weak solutions of magnetohydrodynamic equations near boundary in dimension three. We prove that suitable weak solutions are Hölder continuous near boundary provided that either the scaled L^p,q_x,t-norm of the velocity with 3/p+2/q≤ 2, 2<q<∞, or the scaled L^p,q_x,t-norm of the vorticity with 3/p+2/q≤ 3, 2<q<∞ are sufficiently small near the boundary.

Citations

• Some mathematical questions related to the mhd equations

Cited by

• Partial regularity of suitable weak solutions to the incompressible magnetohydrodynamic equations

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