On the vanishing electron-mass limit in plasma hydrodynamics in unbounded media

TL;DR

This paper analyzes the zero-electron-mass limit in plasma hydrodynamics, demonstrating convergence to incompressible fluid models under specific conditions using advanced mathematical techniques.

Contribution

It establishes the asymptotic behavior of the Navier-Stokes-Poisson system in unbounded domains, connecting it to incompressible fluid equations with damping or without, depending on viscosity.

Findings

Limit is the incompressible Navier-Stokes with Brinkman damping when viscosity is proportional to electron mass.

Limit is the incompressible Euler system when viscosity is dominated by electron mass.

Uses RAGE theorem and dispersive estimates for acoustic waves in the proof.

Abstract

We consider the zero-electron-mass limit for the Navier-Stokes-Poisson system in unbounded spatial domains. Assuming smallness of the viscosity coefficient and ill-prepared initial data, we show that the asymptotic limit is represented by the incompressible Navier-Stokes system, with a Brinkman damping, in the case when viscosity is proportional to the electron-mass, and by the incompressible Euler system provided the viscosity is dominated by the electron mass. The proof is based on the RAGE theorem and dispersive estimates for acoustic waves, and on the concept of suitable weak solutions for the compressible Navier-Stokes system.