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Entropy in Exact 2D Navier-Stokes and 3D Burgers Gas Flows
1Department of Mathematical and Physical Sciences, La Trobe University, Bundoora, VIC 3086, Australia.
Abstract:
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.
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