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Incompressible Limit for Compressible Fluids with Stochastic Forcing

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Abstract

We study the asymptotic behavior of the isentropic Navier–Stokes system driven by a multiplicative stochastic forcing in the compressible regime, where the Mach number approaches zero. Our approach is based on the recently developed concept of a weak martingale solution to the primitive system, uniform bounds derived from a stochastic analogue of the modulated energy inequality, and careful analysis of acoustic waves. A stochastic incompressible Navier–Stokes system is identified as the limit problem.

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Authors and Affiliations

  1. Department of Mathematics, Heriot-Watt University, Riccarton Edinburgh, EH14 4AS, UK

    Dominic Breit

  2. Institute of Mathematics AS CR Žitná 25 CZ, Praha 1, 115 67, Czech Republic

    Eduard Feireisl

  3. Technical University Berlin, Institute of Mathematics, Straße des 17. Juni 136, 10623, Berlin, Germany

    Martina Hofmanová

Authors
  1. Dominic Breit
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  2. Eduard Feireisl
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  3. Martina Hofmanová
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Corresponding author

Correspondence to Dominic Breit.

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Communicated by P. Constantin

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Breit, D., Feireisl, E. & Hofmanová, M. Incompressible Limit for Compressible Fluids with Stochastic Forcing. Arch Rational Mech Anal 222, 895–926 (2016). https://doi.org/10.1007/s00205-016-1014-y

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  • DOI: https://doi.org/10.1007/s00205-016-1014-y

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