On a stochastic version of Prouse model in fluid dynamics

A stochastic version of a modified Navier-Stokes equation (introduced by Prouse) is considered in a 3-dimensional torus. We prove existence and uniqueness of martingale solutions. A different model with the non linearity given by a power 5 of the velocity is analyzed; 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.