Global existence of weak solutions for generalized quantum MHD equation

TL;DR

This paper proves the global existence of weak solutions for a generalized quantum magnetohydrodynamics (MHD) equation in two dimensions, using approximation and energy methods for large initial data.

Contribution

It establishes the existence of global weak solutions for the generalized quantum MHD equations in 2D, extending previous results to large initial data and general adiabatic exponents.

Findings

Existence of global weak solutions for the generalized quantum MHD equation.

Applicable to large initial data in a 2D periodic domain.

Uses three-level approximation and energy estimates for proof.

Abstract

We prove the existence of a weak solution to a generalized quantum MHD equation in a 2-dimensional periodic box for large initial data. The existence of a global weak solution is established through a three-level approximation, energy estimates, and weak convergence for the adiabatic exponent \gamma>1.