Entropy in Exact 2D Navier–Stokes and 3D Burgers Gas Flows

Two exact solutions are constructed for viscous compressible gas dynamics in two and three dimensions. The first is a steady vortex, with explicit solutions for the full Navier–Stokes system of velocity, density, temperature and pressure. In contrast, the second is a time-dependent radial solution to the 3D vector Burgers’ equation, with a constant injection rate from a spherical interior surface. That solution is shock-like at low Reynolds numbers. In both cases, expressions are given for the local density of entropy production.