Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1156451 | Stochastic Processes and their Applications | 2008 | 28 Pages |
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 −ν△u−ν△u of the Navier–Stokes equations there is a nonlinear term −△Φ(u)−∇divΦ(u). 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 Φ(u)=ν|u|4uΦ(u)=ν|u|4u, 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.
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Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
B. Ferrario, F. Flandoli,