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Multi-scale Analysis of Compressible Viscous and Rotating Fluids

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Abstract

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.

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Authors and Affiliations

  1. Institute of Mathematics of the Academy of Sciences of the Czech Republic, Žitná 25, 115 67, Praha 1, Czech Republic

    Eduard Feireisl

  2. Institut de Mathématiques UMR 7586, Université Paris Diderot, 175, Rue de Chevaleret, 75013, Paris, France

    Isabelle Gallagher & David Gerard-Varet

  3. IMATH Université du Sud Toulon-Var, BP 20132, 83957, La Garde, France

    Antonín Novotný

Authors
  1. Eduard Feireisl
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  2. Isabelle Gallagher
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  3. David Gerard-Varet
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  4. Antonín Novotný
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Corresponding author

Correspondence to Isabelle Gallagher.

Additional information

Communicated by P. Constantin

The work was supported by Grant 201/09/ 0917 of GA ČR as a part of the general research programme of the Academy of Sciences of the Czech Republic, Institutional Research Plan AV0Z10190503.

The work was partially supported by the A.N.R grant ANR-08-BLAN-0301-01 “Mathocéan”, as well as the Institut Universitaire de France.

The work was partially supported by the A.N.R grant ANR-08-JCJC-0104 “RUGO”.

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Feireisl, E., Gallagher, I., Gerard-Varet, D. et al. Multi-scale Analysis of Compressible Viscous and Rotating Fluids. Commun. Math. Phys. 314, 641–670 (2012). https://doi.org/10.1007/s00220-012-1533-9

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  • DOI: https://doi.org/10.1007/s00220-012-1533-9

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