Noise in fluid dynamics: a personal perspective

Noise plays a fundamental role in fluid dynamics: already in the 19th century, J. Boussinesq conjectured that the turbulent character of fluids should be captured by a stochastic description. In recent years, a particular noise of transport type has received substantial attention in the literature and in this talk we will review a selection of results: on the one hand, a scaling limit under which the noise delays potential blow-up by enhancing diffusion of the system; on the other hand, the method of convex integration giving rise to non-uniqueness of stochastic solutions. Finally we will touch upon corresponding future research directions.