There exist complex behavior of the solution to the 1D compressible Navier-Stokes equations in half space. We find an interesting phenomenon on the solution to 1D compressible isentropic Navier-Stokes equations with constant viscosity coefficient on , that is, the solutions to the initial boundary value problem to 1D compressible Navier-Stokes equations in half space can be transformed to the solution to the Riccati differential equation under some suitable conditions.

中文翻译：

---

一维可压缩Navier-Stokes方程的解析解

在半空间中，一维可压缩Navier-Stokes方程的解存在复杂的行为。在具有恒定粘度系数的一维可压缩等熵Navier-Stokes方程的解上找到一个有趣的现象，即，在半空间的解决方案，以初始边界值问题至1D可压缩Navier-Stokes方程可以转化为一些合适的条件下解决的Riccati微分方程。