On the Steady Magnetohydrodynamic Equations with Nonhomogeneous Boundary Conditions

TL;DR

This paper investigates the stability, solution existence, and topological structure of steady Magnetohydrodynamic equations with nonhomogeneous boundary conditions in multi-connected domains, using Morse-Sard theorem on Sobolev spaces.

Contribution

It provides new insights into the stability and existence of solutions for steady MHD equations with varying parameters and boundary conditions in complex domains.

Findings

Solutions exist for fixed viscosity and resistivity.

Topological structure stability is established.

Connections between solution properties and Morse-Sard theorem are demonstrated.

Abstract

We study both the topological structure stability and the relations of the steady Magnetohydrodynamic equations when $\nu,\eta$ are given different values in muti-connected bounded domain. We also show the solutions's existence for fixed $\nu, \eta.$ The theoretical is the Morse-Sard theorem on Sobolev spaces.