Magneto-hydrodynamical Model for Plasma

TL;DR

This paper introduces a new 3D incompressible magneto-hydrodynamics model for plasma based on fundamental physics equations and proves the existence of weak solutions using the Galerkin method.

Contribution

It develops a novel MHD model for plasma and establishes the existence of weak solutions, advancing theoretical understanding of plasma dynamics.

Findings

Existence of weak solutions proved for the new MHD model

Model derived from Newton's laws and Maxwell equations

Provides a mathematical foundation for plasma simulations

Abstract

Based on the Newton's second law and the Maxwell equations for the electromagnetic fields, we establish a new 3D incompressible magneto-hydrodynamics(MHD) equations for the motion of plasma under the standard Coulomb gauge. By using the Galerkin method, we prove a result on the existence of weak solutions for the new model.