本项目致力于研究当粘性系数和热传导系数依赖于温度时，非等熵可压Navier-Stokes方程的真空自由边界问题的强解适定性。该方程可用以模拟被真空包裹的非等熵粘性气体的运动，并可以进一步地研究宇宙中气态星体的演变。该研究在数学理论与物理应用等邻域都有着重要的意义。.本项目计划建立相应方程的一维和高维的强解局部适定性理论，并研究其自相似解的渐进稳定性。该研究结果将把已有的常数粘性系数和热传导系数情形推广的结果到更具物理背景的情形，即粘性系数和热传导系数依赖于温度的情形。该研究方法会为今后更多的退化抛物型方程真空自由边界问题的研究提供参考价值。

This project is devoted to studying the well-posedness of the strong solutions to the vacuum free boundary problem of the non-isentropic compressible Navier-Stokes equations, where the viscosities and heat conductivity all depend on the temperature. These equations capture the motions of the non-isentropic viscous gas surrounded by the vacuum, and can further study the motions of gaseous stars in the universe. This study is of great importance both in the mathematical theory and physical applications..This project plans to construct the one-dimensional and multi-dimensional local well-posedness theory of strong solutions to the corresponding equations, and to prove the asymptotic stability of the self-similar solutions. The result will extend the previous one, the case that the viscosities and heat conductivity are constants, to the more physical one, the case that the viscosities and heat conductivity depend on the temperature. The methods used in the project have a certain reference value in the study of the vacuum free boundary problem of the degenerate parabolic equations in future.