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Compressible Navier–Stokes Equations on Thin Domains

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Abstract

We consider the barotropic Navier–Stokes system describing the motion of a compressible viscous fluid confined to a straight layer \({\Omega_\varepsilon = \omega\times (0, \varepsilon)}\) , where ω is a particular 2-D domain (a periodic cell, bounded domain or the whole 2-D space). We show that the weak solutions in the 3D domain converge to a (strong) solutions of the 2-D Navier–Stokes system on ω as \({\varepsilon \to 0}\) on the maximal life time of the strong solution.

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Authors and Affiliations

  1. IMATH, EA 2134, Université du Sud Toulon-Var, BP 20132, 83957, La Garde, France

    David Maltese & Antonín Novotný

Authors
  1. David Maltese
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  2. Antonín Novotný
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Corresponding author

Correspondence to David Maltese.

Additional information

Communicated by E. Feireisl

A. Novotný work was supported by the MODTERCOM project within the APEX programme of the region Provence-Alpe-Côte d’Azur.

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Maltese, D., Novotný, A. Compressible Navier–Stokes Equations on Thin Domains. J. Math. Fluid Mech. 16, 571–594 (2014). https://doi.org/10.1007/s00021-014-0177-2

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  • DOI: https://doi.org/10.1007/s00021-014-0177-2

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