AREGBA-DRIOLLET, Denise; BRULL, Stéphane; PENG, Yue-Jun

doi:10.1137/20M1353812

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AREGBA-DRIOLLET, Denise
Institut Polytechnique de Bordeaux [Bordeaux INP]
Institut de Mathématiques de Bordeaux [IMB]

BRULL, Stéphane
Institut Polytechnique de Bordeaux [Bordeaux INP]
Institut de Mathématiques de Bordeaux [IMB]

PENG, Yue-Jun
Laboratoire de Mathématiques Blaise Pascal [LMBP]

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SIAM Journal on Mathematical Analysis. 2021, vol. 53, n° 2, p. 1886-1907

Society for Industrial and Applied Mathematics

Résumé en anglais

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, 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.< Réduire

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non-conservative hyperbolic system

partial dissipation

symmetrization

energy estimates

Euler type model for plasmas AMS subject classifications. 35L60

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GLOBAL EXISTENCE OF SMOOTH SOLUTIONS FOR A NON-CONSERVATIVE BITEMPERATURE EULER MODEL *

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