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Robustness of strong solutions to the compressible Navier-Stokes system

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Abstract

We consider the Navier-Stokes system describing the time evolution of a compressible barotropic fluid confined to a bounded spatial domain in the 3-D physical space, supplemented with the Navier’s slip boundary conditions. It is shown that the class of global in time strong solutions is robust with respect to small perturbations of the initial data. Explicit qualitative estimates are given also in terms of the shape of the underlying physical domain, with applications to problems posed on thin cylinders.

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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. Department of Mathematics Education, Mokpo National University, Muan, 534-729, South Korea

    Bum Ja Jin

  4. 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. Bum Ja Jin
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  4. Antonín Novotný
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Corresponding author

Correspondence to Peter Bella.

Additional information

The research of E. Feireisl leading to these results has received funding from the European Research Council under the European Union’s Seventh Framework Programme (FP7/2007-2013)/ ERC Grant Agreement 320078. The Institute of Mathematics of the Academy of Sciences of the Czech Republic is supported by RVO:67985840.

A. Novotný acknowledges the support of the project MODTERCOM within the APEX programme of the Provence-Alpes-Cote d’Azur region.

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Bella, P., Feireisl, E., Jin, B.J. et al. Robustness of strong solutions to the compressible Navier-Stokes system. Math. Ann. 362, 281–303 (2015). https://doi.org/10.1007/s00208-014-1119-2

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  • DOI: https://doi.org/10.1007/s00208-014-1119-2

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