Vanishing dielectric constant regime for the Navier Stokes Maxwell equations

TL;DR

This paper proves that solutions of the Navier-Stokes-Maxwell equations converge to classical 2D MHD solutions as the dielectric constant approaches zero, using higher-order energy estimates.

Contribution

It rigorously justifies the vanishing dielectric constant limit for the Navier-Stokes-Maxwell equations in 2D, connecting electromagnetic and fluid dynamics models.

Findings

Convergence of solutions as dielectric constant tends to zero

Higher-order energy estimates establish the limit rigorously

Bridges Navier-Stokes-Maxwell and MHD equations in 2D

Abstract

In this paper we rigorously justify the convergence of smooth solutions of the Navier-Stokes-Maxwell equations towards smooth solutions of the classical $2D$ parabolic MHD equations in the case of vanishing dielectric constant . The result is achieved by means of higher-order energy estimates.