The dissipation properties of transport noise

In 2017 Lucio Galeati understood that a suitable scaling limit of certain hyperbolic PDEs with noise may lead to deterministic parabolic equations. Since then, in collaboration with Lucio and Dejun Luo, we have understood the phenomenon from several viewpoints and for different models. Among the consequences there is mixing, enhanced dissipation, delayed blow-up due to noise for several classes of equations including Euler and Navier-Stokes equations, Keller-Siegel and reaction diffusion equations; and also rigorous results on eddy viscosity and eddy dissipation in turbulent fluids have been proved. Along with arguments of stochastic model reduction, developed with Umberto Pappalettera, a picture arises of the potential effects of small scale fluctuations on large scale properties of turbulent fluids.