On the convergence to the Navier-Stokes-Maxwell system with solenoidal Ohm's law

TL;DR

This paper rigorously proves the convergence of the two-fluid incompressible Navier-Stokes-Maxwell system to the system with solenoidal Ohm's law as the momentum transfer coefficient approaches zero, using frequency envelope techniques.

Contribution

It provides a rigorous proof of the asymptotic limit without loss of regularity, advancing understanding of the Navier-Stokes-Maxwell system's behavior.

Findings

Established convergence without regularity loss

Applied frequency envelope method to the limit analysis

Clarified the asymptotic behavior of the two-fluid system

Abstract

The incompressible Navier-Stokes-Maxwell system with solenoidal Ohm's law can be viewed as as the asymptotic limit of the two-fluid incompressible Navier-Stokes-Maxwell system as the momentum transfer coefficient tends to zero (see [1], Ars\'enio, Ibrahim and Masmoudi, Arch. Ration. Mech. Anal., 2015). We prove this limit rigorously without loss of regularity by using the idea of frequency envelope.