相对论流体力学势流方程的精确解
Exact Solutions of the Equations of Relativistic Hydrodynamics Representing Potential Flows
摘要：
我们使用相对论流体力学和标量场理论之间的连接，以产生精确的解析解描述非定常非均匀流动的理想流体与单参数状态方程（EOS）$p = p(ε)$。对于线性状态方程$p = κε$，我们得到了自相似的解决方案的情况下，平面，圆柱和球对称。在极刚性状态方程（$κ=1$）的情形下，我们得到了“双极+偶极”和“双极+四极”轴对称解.我们还发现了一些非线性的EOS承认解析解。
英文摘要：
We use a connection between relativistic hydrodynamics and scalar field theory to generate exact analytic solutions describing non-stationary inhomogeneous flows of the perfect fluid with one-parametric equation of state (EOS) $p = p(ε)$. For linear EOS $p = κε$ we obtain self-similar solutions in the case of plane, cylindrical and spherical symmetries. In the case of extremely stiff EOS ($κ=1$) we obtain ''monopole + dipole'' and ''monopole + quadrupole'' axially symmetric solutions. We also found some nonlinear EOSs that admit analytic solutions.
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