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Dimension Reduction for Compressible Viscous Fluids

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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), Q⊂R 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.

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Authors and Affiliations

  1. Max Planck Institute for Mathematics in the Sciences, Inselstrasse 22, 04103, Leipzig, Germany

    Peter Bella

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

    Eduard Feireisl

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

    Antonín Novotný

Authors
  1. Peter Bella
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  2. Eduard Feireisl
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  3. Antonín Novotný
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Corresponding author

Correspondence to Eduard Feireisl.

Additional information

Eduard Feireisl acknowledges the support of the GAČR (Czech Science Foundation) project P201-13-00522S in the framework of RVO: 67985840.

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Bella, P., Feireisl, E. & Novotný, A. Dimension Reduction for Compressible Viscous Fluids. Acta Appl Math 134, 111–121 (2014). https://doi.org/10.1007/s10440-014-9872-5

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