Global Existence of Smooth Solutions for a Nonconservative Bitemperature Euler Model

Abstract

The bitemperature Euler model describes a crucial step of inertial confinement fusion (ICF) when the plasma is quasineutral while ionic and electronic temperatures remain distinct. The model is written as a first-order hyperbolic system in nonconservative form with partially dissipative source terms. We consider the polytropic case for both ions and electrons with different $\gamma$-law pressures. The system does not fulfill the Shizuta--Kawashima condition and, the physical entropy, which is a strictly convex function, does not provide a symmetrizer of the system. In this paper we exhibit a symmetrizer to apply the result on the local existence of smooth solutions in several space dimensions. In the one-dimensional case we establish energy and dissipation estimates leading to global existence for small perturbations of equilibrium states.