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

TL;DR

This paper rigorously derives the compressible Navier-Stokes equations from the two-fluid Navier-Stokes-Maxwell system, providing a mathematical justification for the singular limit under well-prepared initial data.

Contribution

It offers a rigorous derivation and justification of the compressible Navier-Stokes equations from a more complex two-fluid system, including uniform error decay analysis.

Findings

Successful derivation of the Navier-Stokes equations from two-fluid equations

Proof of uniform decay of the error system

Validation of the singular limit under specific initial conditions

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.