Stochastic compressible Euler equations and inviscid limits

Dominic Breit; Prince Romeo Mensah

doi:10.1016/j.na.2019.02.013

Stochastic compressible Euler equations and inviscid limits

Dominic Breit, Prince Romeo Mensah

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Abstract

We prove the existence of a unique local strong solution to the stochastic compressible Euler system with nonlinear multiplicative noise. This solution exists up to a positive stopping time and is strong in both the PDE and probabilistic sense. Based on this existence result, we study the inviscid limit of the stochastic compressible Navier–Stokes system. As the viscosity tends to zero, any sequence of finite energy weak martingale solutions converges to the compressible Euler system.

Original language	English
Pages (from-to)	218-238
Number of pages	21
Journal	Nonlinear Analysis: Theory, Methods and Applications
Volume	184
Early online date	5 Mar 2019
DOIs	https://doi.org/10.1016/j.na.2019.02.013
Publication status	Published - Jul 2019

Keywords

Compressible fluids
Euler system
Inviscid limit
Local strong solutions
Navier–stokes Navier–Stokes system
Stochastic forcing

ASJC Scopus subject areas

Analysis
Applied Mathematics

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title = "Stochastic compressible Euler equations and inviscid limits",

abstract = "We prove the existence of a unique local strong solution to the stochastic compressible Euler system with nonlinear multiplicative noise. This solution exists up to a positive stopping time and is strong in both the PDE and probabilistic sense. Based on this existence result, we study the inviscid limit of the stochastic compressible Navier–Stokes system. As the viscosity tends to zero, any sequence of finite energy weak martingale solutions converges to the compressible Euler system. ",

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AU - Breit, Dominic

AU - Mensah, Prince Romeo

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N2 - We prove the existence of a unique local strong solution to the stochastic compressible Euler system with nonlinear multiplicative noise. This solution exists up to a positive stopping time and is strong in both the PDE and probabilistic sense. Based on this existence result, we study the inviscid limit of the stochastic compressible Navier–Stokes system. As the viscosity tends to zero, any sequence of finite energy weak martingale solutions converges to the compressible Euler system.

AB - We prove the existence of a unique local strong solution to the stochastic compressible Euler system with nonlinear multiplicative noise. This solution exists up to a positive stopping time and is strong in both the PDE and probabilistic sense. Based on this existence result, we study the inviscid limit of the stochastic compressible Navier–Stokes system. As the viscosity tends to zero, any sequence of finite energy weak martingale solutions converges to the compressible Euler system.

KW - Compressible fluids

KW - Euler system

KW - Inviscid limit

KW - Local strong solutions

KW - Navier–stokes Navier–Stokes system

KW - Stochastic forcing

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U2 - 10.1016/j.na.2019.02.013

DO - 10.1016/j.na.2019.02.013

M3 - Article

SN - 0362-546X

VL - 184

SP - 218

EP - 238

JO - Nonlinear Analysis: Theory, Methods and Applications

JF - Nonlinear Analysis: Theory, Methods and Applications

ER -

Stochastic compressible Euler equations and inviscid limits

Abstract

Keywords

ASJC Scopus subject areas

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