This paper is a first attempt to describe the quasineutral limit for a Navier-Stokes-Poisson system where the thermal effects are taken into consideration. In the framework of weak solutions and ill-prepared data, we show that as λ → 0 the velocity field u λ strongly converges towards an incompressible velocity vector field u, the density fluctuation n λ − 1 weakly converges to zero and the temperature equation converges towards the so called Fourier equation. We shall provide a detailed mathematical description of the convergence process by analyzing the acoustic equations, by using microlocal defect measures and by developing an explicit correctors analysis.

The Quasineutral Limit for the Navier-Stokes-Fourier-Poisson System

PIERANGELO
2014

Abstract

This paper is a first attempt to describe the quasineutral limit for a Navier-Stokes-Poisson system where the thermal effects are taken into consideration. In the framework of weak solutions and ill-prepared data, we show that as λ → 0 the velocity field u λ strongly converges towards an incompressible velocity vector field u, the density fluctuation n λ − 1 weakly converges to zero and the temperature equation converges towards the so called Fourier equation. We shall provide a detailed mathematical description of the convergence process by analyzing the acoustic equations, by using microlocal defect measures and by developing an explicit correctors analysis.
978-3-642-39006-7
Quasineutral limit; Navier Stokes Poisson; Defect measures
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.12571/1237
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