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

• Published in: Acta mathematica scientia Vol. 35; no. 1; pp. 1 - 44
• Main Author: 唐平凡 方北香 王亚光
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 2015; Department of Mathematics, and MOE-LSC, Shanghai Jiao Tong University, Shanghai 200240, China
• Subjects: 35L45; 35L67; 35Q20; 35Q31; 76N10; Computational fluid dynamics; Density; Euler-Boltzmann equations; Fluid flow; Hydrodynamics; Lipschitz连续; Mathematical analysis; Mathematical models; radiation hydrodynamics; Riemann problems; Shock waves; Structural stability; 一维; 欧拉方程; 波尔兹曼方程; 流体力学模型; 玻耳兹曼方程; 结构稳定性; 辐射流体力学; radiation hydrodynamics; Euler-Boltzmann equations; 35Q31; 35Q20; Riemann problems; 35L45; 35L67; 76N10; shock waves
• ISSN: 0252-9602; 1572-9087
• DOI: 10.1016/S0252-9602(14)60137-5

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 equations. 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 exists 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.