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Global Existence of Smooth Solutions for a Nonconservative Bitemperature Euler Model
SIAM Journal on Mathematical Analysis ( IF 2 ) Pub Date : 2021-04-01 , DOI: 10.1137/20m1353812
Denise Aregba-Driollet , Stéphane Brull , Yue-Jun Peng

SIAM Journal on Mathematical Analysis, Volume 53, Issue 2, Page 1886-1907, January 2021.
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.


中文翻译:

非保守双温欧拉模型光滑解的整体存在

SIAM数学分析杂志,第53卷,第2期,第1886-1907页,2021年1月。
当等离子体为准中性而离子温度和电子温度保持不同时,双温欧拉模型描述了惯性约束聚变(ICF)的关键步骤。该模型以具有部分耗散源项的非保守形式写为一阶双曲系统。我们考虑离子和电子具有不同的\γ律压时的多变情况。该系统不满足Shizuta-Kawashima条件,并且物理熵是严格的凸函数,不能提供系统的对称性。在本文中,我们展示了一个对称器,可将结果应用于多个空间维上的光滑解的局部存在。在一维情况下,我们建立能量和耗散估计,从而导致平衡状态的微小扰动导致全局存在。
更新日期:2021-04-01
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