by: Dan Crisan, (Imperial College London)

Abstract: For a class of evolution equations that possibly have only local solutions, we introduce a stochastic component that ensures that the solutions of the corresponding stochastically perturbed equations are global. The class of partial differential equations amenable for this type of treatment includes the 3D Navier-Stokes equation, the rotating shallow water equation (viscous and inviscid), 3D Euler equation (in vorticity form), 2D Burgers' equation and many other fluid dynamics models. This is based on joint work with Oana Lang (Babes-Bolyai University). (https://arxiv.org/abs/2403.05923Link opens in a new window)