Differential and Integral Equations

Global existence of martingale solutions to the three-dimensional stochastic compressible Navier-Stokes equations

Dehua Wang and Huaqiao Wang

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Abstract

The stochastic three-dimensional compressible Navier-Stokes equations are considered in a bounded domain with multiplicative noise. The global existence of martingale solution is established through the Galerkin approximation method, stopping time, compactness method and the Jakubowski-Skorokhod theorem. A martingale solution is a weak solution for the fluid variables and the Brownian motion on a probability space. The initial data is arbitrarily large and satisfies a natural compatibility condition.

Article information

Source
Differential Integral Equations, Volume 28, Number 11/12 (2015), 1105-1154.

Dates
First available in Project Euclid: 18 August 2015

Permanent link to this document
https://projecteuclid.org/euclid.die/1439901044

Mathematical Reviews number (MathSciNet)
MR3385137

Zentralblatt MATH identifier
1374.60119

Subjects
Primary: 35Q35: PDEs in connection with fluid mechanics 76N10: Existence, uniqueness, and regularity theory [See also 35L60, 35L65, 35Q30] 76W05: Magnetohydrodynamics and electrohydrodynamics

Citation

Wang, Dehua; Wang, Huaqiao. Global existence of martingale solutions to the three-dimensional stochastic compressible Navier-Stokes equations. Differential Integral Equations 28 (2015), no. 11/12, 1105--1154. https://projecteuclid.org/euclid.die/1439901044


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