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Incompressible Limit for Compressible Fluids with Stochastic Forcing

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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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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Mathematics Subject Classification

  • 60H15
  • 35R60
  • 76N10
  • 35Q30