Global Solutions of the Compressible Euler-Poisson Equations for Plasma with Doping Profile for Large Initial Data of Spherical Symmetry

Abstract

We establish the global-in-time existence of solutions of finite relative-energy for the multidimensional compressible Euler-Poisson equations for plasma with doping profile for large initial data of spherical symmetry. Both the total initial energy and the initial mass are allowed to be {\it unbounded}, and the doping profile is allowed to be of large variation. This is achieved by adapting a class of degenerate density-dependent viscosity terms, so that a rigorous proof of the inviscid limit of global weak solutions of the Navier-Stokes-Poisson equations with the density-dependent viscosity terms to the corresponding global solutions of the Euler-Poisson equations for plasma with doping profile can be established. New difficulties arise when tackling the non-zero varied doping profile, which have been overcome by establishing some novel estimates for the electric field terms so that the neutrality assumption on the initial data is avoided. In particular, we prove that no concentration is formed in the inviscid limit for the finite relative-energy solutions of the compressible Euler-Poisson equations with large doping profiles in plasma physics.