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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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https://hal.uca.fr/hal-03660274
Contributor : Yue-Jun Peng Connect in order to contact the contributor
Submitted on : Thursday, May 5, 2022 - 4:39:16 PM
Last modification on : Saturday, May 7, 2022 - 3:35:07 AM

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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, Society for Industrial and Applied Mathematics, 2021, 53 (2), pp.1886-1907. ⟨10.1137/20M1353812⟩. ⟨hal-03660274⟩

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