On a simplified model for radiating flows

Raphaël Danchin (1) , Bernard Ducomet

1 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées

We consider a simpli ed model arising in radiation hydrodynamics which is based on the barotropic Navier-Stokes system describing the macroscopic uid motion, and a P1-approximation (see below) of the transport equation modeling the propagation of radiative intensity. We establish global-in-time existence of strong solutions for the associated Cauchy problem when initial data are close to a stable radiative equilibrium, and local existence for large data with no vacuum. All our results are stated in the so-called critical Besov spaces.

Domaines: Equations aux dérivées partielles [math.AP]

Raphaël Danchin, Bernard Ducomet. On a simplified model for radiating flows. Journal of Evolution Equations, 2014, 14 (1), pp.155-195. ⟨10.1007/s00028-013-0211-5⟩. ⟨hal-00795422⟩