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Journal Articles SIAM Journal on Mathematical Analysis Year : 2021

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 non-conservative form with partially dissipative source terms. We consider the polytropic case for both ions and electrons with different γ-law pressures. The system does not fulfill the Shizuta-Kawashima condition and the physical entropy, which is a strictly convex function, doses 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.
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Dates and versions

hal-03660274 , version 1 (05-05-2022)

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Denise Aregba-Driollet, Stéphane Brull, Yue-Jun Peng. Global Existence of Smooth Solutions for a Nonconservative Bitemperature Euler Model. SIAM Journal on Mathematical Analysis, 2021, 53 (2), pp.1886-1907. ⟨10.1137/20M1353812⟩. ⟨hal-03660274⟩
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