Global existence of weak solutions for quantum MHD equations

TL;DR

This paper proves the global existence of weak solutions for quantum magnetohydrodynamic equations with density-dependent coefficients, using Faedo-Galerkin and compactness methods, and explores the low Planck limit in a 3D torus.

Contribution

It establishes the global existence of weak solutions for quantum MHD equations with density-dependent viscosity and magnetic diffusion, and analyzes the low Planck limit for large initial data.

Findings

Global weak solutions exist for the quantum MHD equations.

The solutions are valid for large initial data.

The low Planck limit is analyzed in a 3D torus.

Abstract

In this paper, we consider the quantum MHD equations with both the viscosity coefficient and the magnetic diffusion coefficient are depend on the density. we prove the global existence of weak solutions and perform the lower planck limit in a 3-dimensional torus for large initial data. The global existence is shown by using Faedo-Galerkin method and weak compactness techniques for the adiabatic exponent $\gamma>1$.