Uniformly Global Smooth Solutions and Convergence of Euler--Poisson Systems with Small Parameters

Abstract

We consider an Euler--Poisson system with small parameters arising in the modeling of unmagnetized plasmas and semiconductors. For initial data close to constant equilibrium states, we prove the uniformly global existence of smooth solutions with respect to the parameters. This result allows us to show the global-in-time convergence of the Euler--Poisson system as each of the parameters goes to zero. The proof is based on unified energy estimates which are valid for all the parameters. The smallness conditions on the initial data are given explicitly in terms of the parameters.