GLOBAL EXISTENCE OF SMOOTH SOLUTIONS FOR A NON-CONSERVATIVE BITEMPERATURE EULER MODEL *
AREGBA-DRIOLLET, Denise
Institut Polytechnique de Bordeaux [Bordeaux INP]
Institut de Mathématiques de Bordeaux [IMB]
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]
Institut Polytechnique de Bordeaux [Bordeaux INP]
Institut de Mathématiques de Bordeaux [IMB]
AREGBA-DRIOLLET, Denise
Institut Polytechnique de Bordeaux [Bordeaux INP]
Institut de Mathématiques de Bordeaux [IMB]
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]
< Reduce
Institut Polytechnique de Bordeaux [Bordeaux INP]
Institut de Mathématiques de Bordeaux [IMB]
Language
en
Article de revue
This item was published in
SIAM Journal on Mathematical Analysis. 2021, vol. 53, n° 2, p. 1886-1907
Society for Industrial and Applied Mathematics
English 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 ...Read more >
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.Read less <
English Keywords
non-conservative hyperbolic system
partial dissipation
symmetrization
energy estimates
Euler type model for plasmas AMS subject classifications. 35L60
Origin
Hal imported