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On a stochastic version of Prouse model in fluid dynamics

Author

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  • Ferrario, B.
  • Flandoli, F.

Abstract

A stochastic version of modified Navier-Stokes equations (introduced by Prouse) is considered in a three-dimensional torus; its main feature is that instead of the linear term -[nu][big up triangle, open]u of the Navier-Stokes equations there is a nonlinear term . First, for this equation we prove existence and uniqueness of martingale solutions; then existence of stationary solutions. In the last part of the paper a new model, obtained from Prouse model with the nonlinearity [Phi](u)=[nu]u4u, is analysed; for the structure function of this model, some insights towards an expression similar to that obtained by the Kolmogorov 1941 theory of turbulence are presented.

Suggested Citation

  • Ferrario, B. & Flandoli, F., 2008. "On a stochastic version of Prouse model in fluid dynamics," Stochastic Processes and their Applications, Elsevier, vol. 118(5), pages 762-789, May.
    • Handle: RePEc:eee:spapps:v:118:y:2008:i:5:p:762-789
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