Existence of weak solutions to the three-dimensional density-dependent generalized incompressible magnetohydrodynamic flows

TL;DR

This paper proves the existence of weak solutions for three-dimensional density-dependent incompressible magnetohydrodynamic flows with large data using approximation and weak convergence methods.

Contribution

It establishes the existence of weak solutions for complex MHD equations with density dependence, extending previous results to more general conditions.

Findings

Existence of weak solutions for 3D density-dependent MHD flows.

Applicable to large initial data.

Uses approximation scheme and weak convergence method.

Abstract

In this paper we consider the equations of the unsteady viscous, incompressible, and heat conducting magnetohydrodynamic flows in a bounded three-dimensional domain with Lipschitz boundary. By an approximation scheme and a weak convergence method, the existence of a weak solution to the three-dimensional density dependent generalized incompressible magnetohydrodynamic equations with large data is obtained.