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 Laplacian term 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 of polynomial type 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.

On a stochastic version of Prouse model in fluid dynamics

FERRARIO, BENEDETTA;
2008-01-01

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 Laplacian term 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 of polynomial type 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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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11571/107700
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