Solvability of an inhomogeneous boundary value problem for steady MHD equations

TL;DR

This paper establishes the existence of weak solutions for steady magnetohydrodynamic equations with inhomogeneous boundary conditions, introducing a novel magnetic lifting technique to handle boundary data constraints.

Contribution

It presents a new magnetic lifting construction that enables proving solution existence under optimal boundary data assumptions.

Findings

Existence of weak solutions for steady MHD with inhomogeneous boundary conditions.

A new magnetic lifting method improves boundary data handling.

Results apply under sharp boundary data assumptions.

Abstract

In this paper, we consider the steady MHD equations with inhomogeneous boundary conditions for the velocity and the tangential component of the magnetic field. Using a new construction of the magnetic lifting, we obtain existence of weak solutions under sharp assumption on boundary data for the magnetic field.