## Abstract and Applied Analysis

### On the Stochastic 3D Navier-Stokes-$\alpha$ Model of Fluids Turbulence

#### Abstract

We investigate the stochastic 3D Navier-Stokes-$\alpha$ model which arises in the modelling of turbulent flows of fluids. Our model contains nonlinear forcing terms which do not satisfy the Lipschitz conditions. The adequate notion of solutions is that of probabilistic weak solution. We establish the existence of a such of solution. We also discuss the uniqueness.

#### Article information

Source
Abstr. Appl. Anal., Volume 2009 (2009), Article ID 723236, 27 pages.

Dates
First available in Project Euclid: 16 March 2010

https://projecteuclid.org/euclid.aaa/1268745612

Digital Object Identifier
doi:10.1155/2009/723236

Mathematical Reviews number (MathSciNet)
MR2563999

Zentralblatt MATH identifier
05690911

#### Citation

Deugoue, Gabriel; Sango, Mamadou. On the Stochastic 3D Navier-Stokes- $\alpha$ Model of Fluids Turbulence. Abstr. Appl. Anal. 2009 (2009), Article ID 723236, 27 pages. doi:10.1155/2009/723236. https://projecteuclid.org/euclid.aaa/1268745612

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