On a stochastic version of Prouse model in fluid dynamics

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.