Weak-strong uniqueness and low Mach number limit for a viscous compressible fluid around a rotating body

We study the flow of an isothermal compressible Newtonian fluid around a body that performs a (time-independent) rigid motion. We derive a weak-strong uniqueness principle, and show that in the low Mach number limit, the governing equation is well approximated by the Navier-Stokes equations for incompressible rotating flow. Both results are based on the derivation of a relative energy inequality for weak solutions to this exterior-domain problem.