On the Regularity of Weak Solutions to the Magneto Hydrodynamics System near the curved part of the boundary

TL;DR

This paper establishes local regularity conditions for weak solutions to the magnetohydrodynamics (MHD) system near curved boundary parts, extending classical Navier-Stokes regularity results to MHD.

Contribution

It generalizes the Caffarelli–Kohn–Nirenberg theorem to the MHD system near curved boundary regions.

Findings

Provided sufficient conditions for local regularity of weak solutions near curved boundary parts.

Extended classical regularity criteria from Navier-Stokes to MHD systems.

Applicable to points on the $C^3$-smooth boundary.

Abstract

We prove a sufficient conditions of local regularity of suitable weak solutions to the MHD system for the point from $C^3$-smooth part of the boundary. Our conditions are the generalizing of the Caffarelli--Kohn--Nirenberg theorem for Navier-Stokes equations.