Article ID Journal Published Year Pages File Type
1156451 Stochastic Processes and their Applications 2008 28 Pages PDF
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.

Related Topics
Physical Sciences and Engineering Mathematics Mathematics (General)
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