In this talk we introduce a probabilistic approach to show the existence of initial data with arbitrarily large L²(R³), H^•1/2 (R³) and PM²norms for which a Generalized Navier-Stokes system generate a global regular solution. The main feature of the approach we present is that it is not deterministic: we show that from a certain family of possible large initial data most of them give raise to global regular solutions to a given Generalized Navier-Stokes system.