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Abstract and Applied Analysis
Volume 2009, Article ID 723236, 27 pages
http://dx.doi.org/10.1155/2009/723236
Research Article

On the Stochastic 3D Navier-Stokes-饾浖 Model of Fluids Turbulence

Department of Mathematics and Applied Mathematics, University of Pretoria, Pretoria 002, South Africa

Received 24 June 2009; Accepted 21 October 2009

Academic Editor: Ruediger Landes

Copyright © 2009 Gabriel Deugoue and Mamadou Sango. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Citations to this Article [21 citations]

The following is the list of published articles that have cited the current article.

  • Mamadou Sango, “Density Dependent Stochastic Navier-Stokes Equations With Non-Lipschitz Random Forcing,” Reviews In Mathematical Physics, vol. 22, no. 6, pp. 669–697, 2010. View at PublisherView at Google Scholar
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  • Gabriel Deugoue, and Mamadou Sango, “On the Strong Solution for the 3D Stochastic Leray-Alpha Model,” Boundary Value Problems, vol. 2010, no. 1, pp. 723018, 2010. View at PublisherView at Google Scholar
  • Gabriel Deugoue, and Mamadou Sango, “Weak solutions to stochastic 3D Navier–Stokes-α model of turbulence: α-Asymptotic behavior,” Journal of Mathematical Analysis and Applications, vol. 384, no. 1, pp. 49–62, 2011. View at PublisherView at Google Scholar
  • Paul André Razafimandimby, and Mamadou Sango, “Strong solution for a stochastic model of two-dimensional second grade fluids: Existence, uniqueness and asymptotic behavior,” Nonlinear Analysis: Theory, Methods & Applications, vol. 75, no. 11, pp. 4251–4270, 2012. View at PublisherView at Google Scholar
  • Gabriel Deugoué, Paul André Razafimandimby, and Mamadou Sango, “On the 3-D stochastic magnetohydrodynamic- model,” Stochastic Processes and their Applications, vol. 122, no. 5, pp. 2211–2248, 2012. View at PublisherView at Google Scholar
  • Paul André Razafimandimby, and Mamadou Sango, “On the exponential behaviour of stochastic evolution equations for non-Newtonian fluids,” Applicable Analysis, vol. 91, no. 12, pp. 2217–2233, 2012. View at PublisherView at Google Scholar
  • Paul André Razafimandimby, and Mamadou Sango, “Convergence of a sequence of solutions of the stochastic two-dimensional equations of second grade fluids,” Asymptotic Analysis, vol. 79, no. 3-4, pp. 251–272, 2012. View at PublisherView at Google Scholar
  • Mamadou Sango, “Splitting-up scheme for nonlinear stochastic hyperbolic equations,” Forum Mathematicum, vol. 25, no. 5, pp. 931–965, 2013. View at PublisherView at Google Scholar
  • E. Hausenblas, P. A. Razafimandimby, and M. Sango, “Martingale Solution to Equations for Differential Type Fluids of Grade Two Driven by Random Force of Levy Type,” Potential Analysis, vol. 38, no. 4, pp. 1291–1331, 2013. View at PublisherView at Google Scholar
  • Gabriel Deugoué, and Mamadou Sango, “Strong solutions for the stochastic 3D LANS-α model driven by non-Gaussian Lévy noise,” Stochastics and Dynamics, pp. 1550011, 2014. View at PublisherView at Google Scholar
  • Gabriel Deugoue, and Mamadou Sango, “Convergence for a Splitting-Up Scheme for the 3D Stochastic Navier-Stokes-alpha Model,” Stochastic Analysis and Applications, vol. 32, no. 2, pp. 253–279, 2014. View at PublisherView at Google Scholar
  • Hua Qiu, and Shaomei Fang, “Stochastic simplified bardina turbulent model: Existence of weak solution,” Acta Mathematica Scientia, vol. 34, no. 4, pp. 1041–1054, 2014. View at PublisherView at Google Scholar
  • Hakima Bessaih, and Paul André Razafimandimby, “On the Rate of Convergence of the 2-D Stochastic Leray- $$\alpha $$ α Model to the 2-D Stochastic Navier–Stokes Equations with Multiplicative Noise,” Applied Mathematics & Optimization, 2015. View at PublisherView at Google Scholar
  • Paul André Razafimandimby, and Mamadou Sango, “Existence and large time behavior for a stochastic model of modified magnetohydrodynamic equations,” Zeitschrift für angewandte Mathematik und Physik, 2015. View at PublisherView at Google Scholar
  • Zakaria Idriss Ali, and Mamadou Sango, “A note on weak and strong probabilistic solutions for a stochastic quasilinear parabolic equation of generalized polytropic filtration,” International Journal of Modern Physics B, pp. 1640002, 2016. View at PublisherView at Google Scholar
  • Paul André Razafimandimby, “Grade-two fluids on non-smooth domain driven by multiplicative noise: Existence, uniqueness and regularity,” Journal of Differential Equations, 2017. View at PublisherView at Google Scholar
  • Peng Gao, “The stochastic Korteweg–de Vries equation on a bounded domain,” Applied Mathematics and Computation, vol. 310, pp. 97–111, 2017. View at PublisherView at Google Scholar
  • Manil T. Mohan, “Global strong solutions of the stochastic three dimensional inviscid simplified bardina turbulence model,” Communications on Stochastic Analysis, vol. 12, no. 3, pp. 249–270, 2018. View at PublisherView at Google Scholar
  • Ali Zakaria, “Stochastic system for generalized polytropic filtration,” Mathematical Methods in the Applied Sciences, 2019. View at PublisherView at Google Scholar