# Multiple Scales and Singular Limits for Compressible Rotating Fluids with General Initial Data

Abstract : We study the singular limit of a rotating compressible fluid described by a scaled barotropic Navier-Stokes system, where the Rossby number $= \ep$, the Mach number $= \ep^m$, the {Reynolds number} $= \ep^{-\alpha}$, and the \emph{Froude number} $= \ep^n$ are proportional to a small parameter $\ep \to 0$. The inviscid planar Euler system is identified as the limit problem. The proof is based on the application of the method of relative entropies and careful analysis of oscillatory integrals describing the propagation of Rossby-acoustic waves.
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Journal articles

Cited literature [34 references]

https://hal-univ-tln.archives-ouvertes.fr/hal-00998356
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Submitted on : Sunday, June 1, 2014 - 8:38:28 PM
Last modification on : Tuesday, December 7, 2021 - 3:16:02 PM
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• HAL Id : hal-00998356, version 1

### Citation

Eduard Feireisl, Antonin Novotny. Multiple Scales and Singular Limits for Compressible Rotating Fluids with General Initial Data. Communications in Partial Differential Equations, Taylor & Francis, 2014, 39 (6), pp.1104-1127. ⟨hal-00998356⟩

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