Analytical Solution to 1D Compressible Navier-Stokes Equations

Abstract

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 $\left(x,t\right)\in \left[0,+\infty \right)\times R_{+}$ , 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.