Global weak solutions to the Euler-Boltzmann equations in radiation hydrodynamics

Abstract

The Cauchy problem for the one-dimensional Euler-Boltzmann equations in radiation hydrodynamics is studied. The global weak entropy solutions are constructed using the Godunov finite difference scheme. The global existence of weak entropy solutions in L ∞ with arbitrarily large initial data is established with the aid of the compensated compactness method.

Large-time behavior of the motion of a viscous heat-conducting one-dimensional gas coupled to radiation

“…Moreover using (21) to compute the contribution of the radiative terms boundary terms, we have the final equality…”

“…Concerning the existence of solutions, a proof of local-in-time existence and blow-up of solutions (in the inviscid case) has been recently proposed by Zhong and Jiang [33] (see also the recent papers by Jiang and Wang [20,21] for a 1D related "Euler-Boltzmann" model), moreover a simplified version of the system has been investigated by Golse and Perthame [14].…”

On a model in radiation hydrodynamics

“…The existence of local-in-time solutions and sufficient conditions for blow up of classical solutions in the nonrelativistic inviscid case were obtained by Zhong and Jiang [41], see also the recent papers by Jiang and Wang [26,27] for a related one-dimensional "Euler-Boltzmann" type models. Moreover, a simplified version of the system has been investigated by Golse and Perthame [23], where global existence was proved by means of the theory of nonlinear semi-groups.…”

On an incompressible model in radiation hydrodynamics

“…Our goal in the present paper is to show that the existence theory presented in [5] can be extended to the incompressible Navier-Stokes-Fourier system coupled with radiation. For other references see [6][7][8][9][10][11][12][13][14].…”