Dispersive behaviour in the analysis of acoustic waves and plasma oscillations

The paper reports results on the rigorous analysis of the quasineutral limit for a hydrodynamical models for a hydrodynamical models of viscous plasmas with capillarity effects represented by the Navier Stokes Poisson system in 3-D. A common feature of this kind of limits in the ill prepared data framework is the high plasma oscillations, namely the presence of high frequency time oscillations of the acoustic waves. Moreover and other issuewhich makes the limiting behaviour analysis very hard is the presence of very stiff terms due to the electric field. We shall provide a detailed mathematical description of the different behaviours of the various vector fields acting in our system, what and which are the relationship between high frequency interacting waves, dispersive behaviour and the different roles of time and space oscillations.