QIU Hua , FANG Shao-Mei . STOCHASTIC SIMPLIFIED BARDINA TURBULENT MODEL: EXISTENCE OF WEAK SOLUTION[J]. Acta mathematica scientia, Series B, 2014 , 34(4) : 1041 -1054 . DOI: 10.1016/S0252-9602(14)60068-0

[1] Bardina J, Ferziger J, Reynolds W. Improved subgrid scale models for large eddy simulation. American Institute of Aeronautics and Astronautics Paper, 1980, 80: 80–1357

[2] Layton W, Lewandowski R. On a well-posed turbulence model. Dicrete and Continuous Dyn Sys B, 2006, 6: 111–128

[3] Cao Y, Lunasin E M, Titi E S. Global well-posedness of the three-dimensional viscous and inviscid simplified Bardina turbulence models. Commun Math Sci, 2006, 4: 823–848

[4] Chen S Y, Foias C, Holm D D, et al. Camassa-Holm equations as a closure model for turbulent channel and pipe flow. Phys Rev Lett, 1998, 81: 5338–5341

[5] Chen S Y, Foias C, Holm D D, et al. The Camassa-Holm equations and turbulence. Physica D, 1999, 133: 49–65

[6] Chen S Y, Foias C, Holm D D, et al. A connection between Camassa-Holm equations and turbulent flows in channels and pipes. Phys Fluids, 1999, 11: 2343–2353

[7] Foias C, Holm D D, Titi E S. The three dimensional viscous Camassa-Holm equations and their relation to the Navier-Stokes equations and turbulence theory. J Dyn Diff Eq, 2002, 14: 1–35

[8] Cheskidov A, Holm D D, Olson E, et al. On a Leray- model of turbulence. Proc R Soc Lond Ser A Math Phys Eng Sci, 2005, 461: 629–649

[9] Zhou Y, Fan J S. Global well-posedness of a Bardina model. Appl Math Lett, 2011, 24: 605–607

[10] Guo C, Guo B, Pu X. Random attractors for a stochastic hydrodynamical equation in Heisenberg param-agnet. Acta Math Sci, 2011, 31B(2): 529–540

[11] Pu X, Guo B. Global well-posedness of the stochastic 2D Boussinesq equations with partial viscosity. Acta Math Sci, 2011, 31B(5): 1968–1984

[12] Zhou G, Hou Z. The ergodicity of stochastic generalized porous equations with L’evy jump. Acta Math Sci, 2011, 31B(3): 925–933

[13] Caraballo T, Real J, Taniguchi T. The existence and uniqueness of solutions to stochastic three-dimensional
Lagrangian averaged Navier-Stokes equations. Proc R Soc A, 2006, 462: 459–479

[14] Deugoue G, Sango M. On the stochastic 3D Navier-Stokes- model of fluids turbulence. Abstr Appl Anal, 2009, Article ID 723236, 27 pages

[15] Deugoue G, Sango M. On the strong solution for the 3D stochastic Leray-Alpha model. Bound Value Probl, 2010, Article ID 723018, 31 pages

[16] Temam R. Navier Stokes Equations, Theory and Numerical Analysis. Vol 2 of Studies in Mathematics and Its Applications. 3rd ed. North-Holland, Amsterdam, The Netherlands: North-Holland Publishing Company, 1997

[17] Prohorov Y V. Convergence of random processes and limit theorems in probability theory (in Russian). Teor Veroyatn Primen, 1956, 1: 177–238

[18] Skorokhod A V. Limit theorems for stochastic processes. Teor Veroyatn Primen, 1956, 1: 289–319

[19] Bensoussan A. Stochastic Navier-Stokes equations. Acta Appl Math, 1995, 38: 267–304

[20] Karatzas I, Shreve S E. Brownian Motion and Stochastic Calculus. Vol 113 of Graduate Texts in Mathe-matics. New York: Springer, 1987

[21] Evans L C. An introduction to stochastic differential equations. Http://math.berkeley.edu/evans

[22] Pardoux E. ´Equations aux D´eriv´ees Partielles Stochastiques Non Lin´eaires Monotones[D]. Paris: Universit´e
Paris XI, 1975

[23] Langa J A, Real J, Simon J. Existence and regularity of the pressure for the stochastic Navier-Stokes equations. Appl Math Opt, 2003, 48: 195–210