Rigorous derivation of the compressible Navier-Stokes equations from the two-fluid Navier-Stokes-Maxwell equations

Abstract

In this paper, we rigorously derive the compressible one-fluid Navier-Stokes equation from the scaled compressible two-fluid Navier-Stokes-Maxwell equations locally in time under the assumption that the initial data are well prepared. We justify the singular limit by proving the uniform decay of the error system, which is obtained by elaborate energy estimates.