Stochastic Stabilization of Fluid Dynamics Models

We introduce a carefully designed stochastic perturbation whose diffusion coefficient depends super-linearly on the solution norm. This noise acts selectively, becoming active when the norm approaches blow-up, and its quadratic variation produces a stabilizing second-order effect. Under suitable structural assumptions on the drift, we prove that the associated SPDE admits global strong solutions almost surely in three regimes of initial regularity. In particular, the stochastic control extends the lifespan of solutions to infinite time, including in situations where no global deterministic solution is known. This is joint work with Dan Crisan, based on the paper Lang, O., Crisan, D. Global solutions for stochastically controlled fluid dynamics models. Stoch PDE: Anal Comp (2025).