Stochastic compressible Euler equations and inviscid limits. (July 2019)

• Record Type: Journal Article
• Authors: Breit, Dominic; Mensah, Prince Romeo
• Is Part Of: Nonlinear analysis. Volume 184(2019)
• Page Start: 218
• Page End: 238
• Publication Date: 2019-07
• Subjects: Euler system -- Navier–Stokes system -- Compressible fluids -- Stochastic forcing -- Local strong solutions -- Inviscid limit; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2019.02.013
• Languages: English
• ISSNs: 0362-546X

Abstract

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.