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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
