Incompressible limit for compressible fluids with stochastic forcing

Dominic Breit; Eduard Feireisl; Martina Hofmanová

doi:10.1007/s00205-016-1014-y

Incompressible limit for compressible fluids with stochastic forcing

Dominic Breit, Eduard Feireisl, Martina Hofmanová

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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 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.

Original language	English
Pages (from-to)	895–926
Number of pages	32
Journal	Archive for Rational Mechanics and Analysis
Volume	222
Issue number	2
Early online date	27 May 2016
DOIs	https://doi.org/10.1007/s00205-016-1014-y
Publication status	Published - Nov 2016

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title = "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 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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AU - Feireisl, Eduard

AU - Hofmanová, Martina

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N2 - 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 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.

AB - 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 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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DO - 10.1007/s00205-016-1014-y

M3 - Article

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EP - 926

JO - Archive for Rational Mechanics and Analysis

JF - Archive for Rational Mechanics and Analysis

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ER -

Incompressible limit for compressible fluids with stochastic forcing

Abstract

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