数学物理学报(英文版) ›› 2015, Vol. 35 ›› Issue (1): 1-44.doi: 10.1016/S0252-9602(14)60137-5

• 论文 •    下一篇

ON LOCAL STRUCTURAL STABILITY OF ONE-DIMENSIONAL SHOCKS IN RADIATION HYDRODYNAMICS

唐平凡|方北香|王亚光   

  1. Department of Mathematics, and MOE-LSC, Shanghai Jiao Tong University, Shanghai 200240, China
  • 收稿日期:2014-01-10 修回日期:2014-05-20 出版日期:2015-01-20 发布日期:2015-01-20
  • 基金资助:

    This work is supported by NNSF of China (10971134, 11031001, 91230102, 11371250).

ON LOCAL STRUCTURAL STABILITY OF ONE-DIMENSIONAL SHOCKS IN RADIATION HYDRODYNAMICS

TANG PingFan, FANG BeiXiang, WANG YAGuang   

  1. Department of Mathematics, and MOE-LSC, Shanghai Jiao Tong University, Shanghai 200240, China
  • Received:2014-01-10 Revised:2014-05-20 Online:2015-01-20 Published:2015-01-20
  • Supported by:

    This work is supported by NNSF of China (10971134, 11031001, 91230102, 11371250).

摘要:

In this paper, we are concerned with the local structural stability of one-dimensional shock waves in radiation hydrodynamics described by the isentropic Euler-Boltzmann equa-tions. Even though in this radiation hydrodynamics model, the radiative effects can be understood as source terms to the isentropic Euler equations of hydrodynamics, in general the radiation field has singularities propagated in an angular domain issuing from the initial point across which the density is discontinuous. This is the major difficulty in the stability analysis of shocks. Under certain assumptions on the radiation parameters, we show there ex-ists a local weak solution to the initial value problem of the one dimensional Euler-Boltzmann equations, in which the radiation intensity is continuous, while the density and velocity are piecewise Lipschitz continuous with a strong discontinuity representing the shock-front. The existence of such a solution indicates that shock waves are structurally stable, at least local in time, in radiation hydrodynamics.

关键词: radiation hydrodynamics, Euler-Boltzmann equations, Riemann problems, shock waves

Abstract:

In this paper, we are concerned with the local structural stability of one-dimensional shock waves in radiation hydrodynamics described by the isentropic Euler-Boltzmann equa-tions. Even though in this radiation hydrodynamics model, the radiative effects can be understood as source terms to the isentropic Euler equations of hydrodynamics, in general the radiation field has singularities propagated in an angular domain issuing from the initial point across which the density is discontinuous. This is the major difficulty in the stability analysis of shocks. Under certain assumptions on the radiation parameters, we show there ex-ists a local weak solution to the initial value problem of the one dimensional Euler-Boltzmann equations, in which the radiation intensity is continuous, while the density and velocity are piecewise Lipschitz continuous with a strong discontinuity representing the shock-front. The existence of such a solution indicates that shock waves are structurally stable, at least local in time, in radiation hydrodynamics.

Key words: radiation hydrodynamics, Euler-Boltzmann equations, Riemann problems, shock waves

中图分类号: 

  • 35L45