标题： 具有奇点的理想流体动力学中非弹性气体的精确解 显示英文标题

标题： Exact solutions with singularities to ideal hydrodynamics of inelastic gases

摘要： 我们构造了一个大族的精确解，这些解适用于理想颗粒流体动力学的三维双曲方程组，在任意绝热指数为$\gamma$的多维情况下。根据初始条件，这些解可以始终保持光滑，或者会形成奇异性。特别是，在二维情况下，奇异性可以在一个点或沿着一条线形成。对于$\gamma=-1$情况，问题可以简化为两个方程组成的系统，这与卡普里金气体的一个特殊情况相关。在一维情况下，该系统可以用里曼不变量表示，并且可以用标准方法处理。在这种情况下，黎曼问题的解表现出非同寻常和复杂的行为。 显示英文摘要

摘要： We construct a large family of exact solutions to the hyperbolic system of 3 equations of ideal granular hydrodynamics in several dimensions for arbitrary adiabatic index $\gamma$. In dependence of initial conditions these solutions can keep smoothness for all times or develop singularity. In particular, in the 2D case the singularity can be formed either in a point or along a line. For $\gamma=-1$ the problem is reduced to the system of two equations, related to a special case of the Chaplygin gas. In the 1D case this system can be written in the Riemann invariant and can be treated in a standard way. The solution to the Riemann problem in this case demonstrate an unusual and complicated behavior.