Analytical Solution to 1D Compressible Navier-Stokes Equations

There exist complex behavior of the solution to 1D compressible Navier-Stokes equations in half space. We find an interesting phenomenon on isentropic with constant viscosity coefficient x , t ∈ open="[" 0 + ∞ × R , that is, solutions initial boundary value problem space can be transformed Riccati differential equation under some suitable conditions.