Incompressible type limit analysis of a hydrodynamic model for charge-carrier transport

TL;DR

This paper rigorously analyzes the zero electron mass limit in a hydrodynamic charge-carrier model, demonstrating convergence to incompressible Navier-Stokes equations even with ill-prepared initial data, using asymptotic and uniform estimate techniques.

Contribution

It provides a rigorous proof of the zero electron mass limit for the Navier-Stokes-Poisson system under general initial conditions, establishing strong convergence to incompressible Navier-Stokes equations.

Findings

Proved zero electron mass limit in Navier-Stokes-Poisson system.

Established strong convergence to incompressible Navier-Stokes equations.

Handled ill-prepared initial data with fast oscillations.

Abstract

This paper is concerned with the rigorous analysis of the zero electron mass limit of the full Navier-Stokes-Poisson. This system has been introduced in the literature by Anile and Pennisi (see [5]) in order to describe a hydrodynamic model for charge-carrier transport in semiconductor devices. The purpose of this paper is to prove rigorously zero electron mass limit in the framework of general ill prepared initial data. In this situation the velocity field and the electronic fields develop fast oscillations in time. The main idea we will use in this paper is a combination of formal asymptotic expansion and rigorous uniform estimates on the error terms. Finally we prove the strong convergence of the full Navier Stokes Poisson system towards the incompressible Navier Stokes equations.