Torstein Nilssen: Noise Prevents Singularities in Linear Transport Equations

The (deterministic) linear transport equation can be solved using flows of an ordinary differential equation. However, if the driving vector field is non-Lipschitz, it can be difficult or impossible to solve the ordinary differential equation. In this talk I will present a method which shows that the corresponding stochastic differential equation possesses a weakly differentiable flow and this leads to a unique solution of the stochastic transport equation when the driving vector field is merely bounded and measurable.