Local Smooth Solution and Non-Relativistic Limit of Radiation Hydrodynamics Equations

Yong Li,Jianwei Yang,Shu Wang

doi:10.1155/2010/716451

Abstract

We investigate a multidimensional nonisentropic radiation hydrodynamics model. We study the local existence and the convergence of the nonisentropic radiation hydrodynamics equations via the non-relativistic limit. The local existence of smooth solutions to both systems is obtained. For well-prepared initial data, the convergence of the limit is rigorously justified by an analysis of asymptotic expansion, an energy method, and an iterative scheme. We also establish uniform a priori estimates with respect to .

Highlights

In this paper, we study a system of PDEs describing radiation-driven perfect compressible flows, in particular in astrophysics cf. 1–4
Assuming that the radiative temperature and the fluid temperature are equal, and that the gas is radiatively opaque so that the equilibrium diffusion will be dealt with, and the mean free path of photons is much smaller than the typical length of the flow, we can write the equations of radiation hydrodynamics without radiative heat diffusivity in Rd, describing the conservation of mass, momentum and energy, as see 2, 3, 5
The convergence of the radiation hydrodynamics equations to the compressible and nonisentropic Euler equations is achieved through the energy estimates for error equations derived from 1.1 and it’s formal limit equations 1.3

Summary

Introduction

We study a system of PDEs describing radiation-driven perfect compressible flows, in particular in astrophysics cf. 1–4. We prove the existence of smooth solutions to the problem 1.1 and their convergence to the solutions of the compressible and nonisentropic Euler equations in a time interval independent of. For this propose, we use the method of iteration scheme and classical energy method. The convergence of the radiation hydrodynamics equations to the compressible and nonisentropic Euler equations is achieved through the energy estimates for error equations derived from 1.1 and it’s formal limit equations 1.3. The final part is devoted to rigorously justifying the asymptotic expansion developed in Section 3 and obtaining the convergence of solutions to the multidimensional compressible nonisentropic Euler system in a time interval independent of. Dxs A v L∞ 1 ∇v L∞ s−1 Dxs v L2 , s ≥ 1

The Local Existence

Formal Asymptotic Expansions

Preliminary

Derivation of Error Equations

Proof of Convergence

C M2 T1 m