Boundary regularity criteria for suitable weak solutions of the magnetohydrodynamic equations

TL;DR

This paper establishes new boundary regularity criteria for suitable weak solutions of 3D magnetohydrodynamic equations, showing H"older continuity under small scaled norms of velocity or vorticity.

Contribution

It introduces novel boundary regularity criteria based on scaled $L^{p,q}_{x,t}$-norms for velocity and vorticity in magnetohydrodynamic equations.

Findings

Suitable weak solutions are H"older continuous near boundary under certain smallness conditions.

Regularity criteria depend on scaled $L^{p,q}_{x,t}$-norms of velocity and vorticity.

Provides conditions for boundary regularity in 3D magnetohydrodynamics.

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 H\"older continuous near boundary provided that either the scaled $L^{p,q}_{x,t}$-norm of the velocity with $3/p+2/q\le 2$, $2<q<\infty$, or the scaled $L^{p,q}_{x,t}$-norm of the vorticity with $3/p+2/q\le 3$, $2<q<\infty$ are sufficiently small near the boundary.