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Acta Applicandae Mathematicae

, Volume 134, Issue 1, pp 111–121 | Cite as

Dimension Reduction for Compressible Viscous Fluids

  • Peter Bella
  • Eduard FeireislEmail author
  • Antonín Novotný
Article

Abstract

We consider the barotropic Navier-Stokes system describing the motion of a compressible viscous fluid confined to a cavity shaped as a thin rod Ω ε =εQ×(0,1), QR 2. We show that the weak solutions in the 3D domain converge to (strong) solutions of the limit 1D Navier-Stokes system as ε→0.

Keywords

Compressible Navier-Stokes system Dimension reduction Thin rod 

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Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  • Peter Bella
    • 1
  • Eduard Feireisl
    • 2
    Email author
  • Antonín Novotný
    • 3
  1. 1.Max Planck Institute for Mathematics in the SciencesLeipzigGermany
  2. 2.Institute of Mathematics of the Academy of Sciences of the Czech RepublicPraha 1Czech Republic
  3. 3.IMATH, EA 2134Université du Sud Toulon-VarLa GardeFrance

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