本项目旨在对具有van der Waals流体状态函数的相对论Euler方程组的亚音速相变开展容许准则，高维稳定性及存在性的研究。. 随着航空、航天等应用领域的飞速发展，高温高速流体的理论研究意义日益重要。在高速流体的运动中，相对论效应是不可忽视的。因此经典力学意义下的Euler方程组应被相对论Euler方程组所取代。如果流体同时处于高温状态，液化汽化等物相变化现象不可避免。非单调的van der Waals类型状态函数可以很好地刻画此现象，同时也带来了新类型的非线性波，亚音速相变。在相对论Euler方程组下，此非线性波的研究对于实际应用有着重要意义，同时在数学理论研究上也提出了有趣的问题。. 我们希望克服传统行波法在此类问题中所面临的困难，为此类非线性波找出其容许准则，并证明其在高维空间中的稳定性和存在性。在此基础上，相对论多相流体可以获得更多的有意义的研究成果。

This project carries out the study of the admissible criterion, multidimensional stability and existence of subsonic phase transitions of the system of relativistic Euler equations with a van der Waals type state function.. With the development of applications in aviation and aerospace, the study of fluid with high temperature and high velocity shows its importance. Relativistic effects play an important role in the motion of a fluid with high velocity. Therefore, the system of relativistic Euler equations is a better way to study this motion than the system of classical Euler equations. Meanwhile, if the fluid is also in high temperature, then phase transitions such as liquidize and vaporize are inevitable, which is properly described by the nonmonotonic state function of van der Waals type. New types of nonlinear waves, say subsonic phase transition, exist in this situation. The study of this kind of nonlinear waves under relativity is important in applications and it also provides interesting problems in mathematics.. We expect to overcome the difficulty of traveling wave method to get the admissible criterion for subsonic phase transition and prove its stabiltiy and existence in high dimensional spaces. Therefore, more interesting results can be developed for relativistic multi-phase fluid.