Incompressible Type Limit Analysis of a Hydrodynamic Model for Charge-Carrier Transport

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 [Phys. Rev. B, 46 (1992), pp. 13186--13193]) 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 toward the incompressible Navier--Stokes equations.

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