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

Denise Aregba-Driollet (1, 2) , Stéphane Brull (1, 2) , Yue-Jun Peng (3)

1 Bordeaux INP - Institut Polytechnique de Bordeaux
2 IMB - Institut de Mathématiques de Bordeaux
3 LMBP - Laboratoire de Mathématiques Blaise Pascal

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.

Mots clés: non-conservative hyperbolic system; partial dissipation; symmetrization; energy estimates; Euler type model for plasmas AMS subject classifications. 35L60

Domaines: Mathématiques [math]

Denise Aregba-Driollet, Stéphane Brull, Yue-Jun Peng. GLOBAL EXISTENCE OF SMOOTH SOLUTIONS FOR A NON-CONSERVATIVE BITEMPERATURE EULER MODEL *. SIAM Journal on Mathematical Analysis, 2021, 53 (2), pp.1886-1907. ⟨10.1137/20M1353812⟩. ⟨hal-03944419⟩