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

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.