辐射流体力学方程组渐近极限的数学理论研究

辐射流体力学研究热辐射在流体中的传播及其对流体运动的影响，在国防建设和科学技术等方面具有重要而广泛的应用。本项目主要围绕辐射流体力学中的若干小参数渐近极限问题开展理论研究，重点研究可压缩Euler-输运耦合方程组与Navier-Stokes-输运耦合方程组光滑解的平衡态或非平衡态扩散近似过程，建立辐射流力学方程组扩散近似过程的严格的数学理论；研究辐射流体力学方程组的小马赫数渐近极限过程,刻画高温辐射流体在低马赫数时的物理状态。本项目的研究将提升对辐射流体力学方程复杂奇异非线性行为的理解，并推动辐射流体力学理论与应用研究的发展。

Radiation hydrodynamics studies the propagation of heating radiation in the fluid flow and its effect on the fluid, and is applied widely in the national defence and technology. The present project is mainly concerned with the mathematical theory of some singular problems arising from radiation hydrodynamics. We focus on the equilibrium diffusion limit or non-equilibrium diffusion limit of smooth solution to the multidimension Euler-transported or Navier-Stokes-transported coupled system, and establish the rigorous mathematical theory of diffusion process for the radiation hydrodynamics. And we also study the low Mach number limit for the radiation hydrodynamics. The aim of the study is to understand the complicated singular behavior of the radiation hydrodynamics, and to develop the theory and the applications of radiation hydrodynamics.