Applied Mathematics Colloquium

Abstract: The current mathematical description of fully developed turbulence is given by the vanishing viscosity limit for the long-time dynamics of the Navier-Stokes equations, away from boundaries. The sensitivity to the initial conditions and to the parameters characterizing any nonlinear system, and in particular the above one, suggests that the longterm dynamics should be described by universal objects (attractors, invariant measures) which capture the essential features of the model and maintain robustness properties with respect to regular, singular and/or stochastic perturbations. We will give a general overview of some recent results concerning stochastically forced linear and nonlinear models and try to highlight the physical aspects connected to a few mathematically rigorous results.