辐射流体力学方程组的数学理论研究是近年来偏微分方程领域研究的热点和重难点问题之一。本项目主要围绕辐射流体力学方程组的适定性、正则性、解的长时间行为以及该方程组的Rayleigh-Taylor不稳定性和粘性消失极限问题展开，重点研究高维无粘辐射流体力学方程组小初值整体解适定性和最优衰减率，以及不同介质中辐射流体力学方程组的 Rayleigh-Taylor不稳定性；研究高维带粘性的辐射流体力学方程组的整体适定性和 Rayleigh-Taylor 不稳定性；研究高维带粘性的辐射流体力学方程组当粘性系数趋于零时的极限问题，以及由这些极限问题所产生的初始层、边界层数学理论分析。所研究内容来源于实际物理问题，具有很强的应用背景，在数学上具有重要的理论意义，且紧密联系应用科学, 具有很强的科学价值和应用价值。

The mathematical studies of the equations of radiation hydrodynamics are one of the hot and difficult issues in the field of PDEs in recent years. This project focuses on well-posedness, regularity, large-time behavior of the solution, Rayleigh-Taylor instability and limit problems of these PDEs, including global well-posedness, the optimal decay of the solution and Rayleigh-Taylor instability in several fluids of different densities for the equations of multidimensional radiation hydrodynamics which are a Euler-Boltzmann coupled system, and global well-posedness, Rayleigh-Taylor instability and limit problems, then the associated analysis of initial and boundary layers for these limit problems for the equations of multidimensional radiation hydrodynamics which are a Navier-Stokes-Boltzmann coupled system. These problems originate from practical problems with strong physical background and introduce many essential mathematical theoretical problems, having high scientific interest and close connections to applied scientific branches.