论文标题
Euler流中的奇异性：多估的解决方案，冲击波和相变
Singularities in Euler flows: multivalued solutions, shock waves, and phase transitions
论文作者
论文摘要
在本文中，我们分析了Euler方程描述的一维气流中的各种类型的临界现象。我们对热力学进行了几何解释，并特别强调相变。我们使用PDE的几何理论的思想，尤其是对称性和差异约束来找到对Euler系统的解决方案。获得的溶液是多价的，具有对自变量平面的投影的奇异性。我们分析了冲击波阵线和相变的传播。
In this paper, we analyze various types of critical phenomena in one-dimensional gas flows described by Euler equations. We give a geometrical interpretation of thermodynamics with a special emphasis on phase transitions. We use ideas from the geometrical theory of PDEs, in particular, symmetries and differential constraints to find solutions to the Euler system. Solutions obtained are multivalued, have singularities of projection to the plane of independent variables. We analyze the propagation of the shock wave front along with phase transitions.
