Analysis of Oscillations and Defect measures in plasma physics

We perform a rigorous analysis of the quasineutral limit for a hy- drodynamical model of a viscous plasma represented by the Navier Stokes Poisson system in 3 − D in the general setting of ill prepared initial data. In general the limit velocity field cannot be expected to satisfy the incompress- ible Navier Stokes equation, indeed the presence of high frequency oscillations strongly affects the quadratic nonlinearities and we have to take care of self in- teracting wave packets. We provide a detailed mathematical description of the convergence process by using microlocal defect measures and by developing an explicit correctors analysis. Moreover we identify an explicit pseudo parabolic pde satisfied by the leading correctors terms.