Vanishing dielectric constant regime for the Navier Stokes Maxwell   equations
  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. 
Donatella Donatelli and Stefano Spirito
math.AP