Multi-scale analysis of compressible viscous and rotating fluids. (English) Zbl 1251.35069
Summary: We study a singular limit for the compressible Navier-Stokes system when the Mach and Rossby numbers are proportional to certain powers of a small parameter \({\varepsilon}\). If the Rossby number dominates the Mach number, the limit problem is represented by the 2-D incompressible Navier-Stokes system describing the horizontal motion of vertical averages of the velocity field. If they are of the same order then the limit problem turns out to be a linear, 2-D equation with a unique radially symmetric solution. The effect of the centrifugal force is taken into account.
MSC:
| 35Q30 | Navier-Stokes equations |
| 76U05 | General theory of rotating fluids |
| 76Nxx | Compressible fluids and gas dynamics |
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