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In this paper, we consider the initial-boundary value problem of three-dimensional isentropic compressible Navier-Stokes equations with rotating effect terms in an exterior domain with Navier-slip boundary condition and with far-field vacuum. This problem is related to the motion of the compressible viscous flow past a rotating obstacle. We establish the global existence and uniqueness of classical solutions, provided that the initial mass is small. The initial data and the angular velocity of the obstacle are allowed to have large oscillations.

We prove the existence and uniqueness of global strong solutions to the free boundary problem in one-dimensional compressible Navier-Stokes system for the viscous and heat-conducting ideal polytropic gas flow, when the viscosity and heat conductivity depend on temperature in power law of Chapman-Enskog and the data are in the neighborhood of some background solution at initial time. We also study the large-time behavior of the solution and obtain its decay property.

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This a preprint and has not been peer reviewed. Data may be preliminary.