Enhanced dissipation for stochastic Navier-Stokes equations with transport noise

The phenomenon of dissipation enhancement by transport noise is shown for stochastic 2D Navier-Stokes equations in velocity form. In the 3D case, suppression of blow-up is proved for stochastic Navier-Stokes equations in vorticity form; in particular, quantitative estimates allow us to choose parameters in the noise so that the blow-up probability is less than any given threshold.