Felix Otto (Max Planck Institute for Mathematics in the Sciences) This talk is about a simple but rich model problem at the cross section of stochastic homogenization and singular stochastic PDE: We consider a drift-diffusion process with a time-independent and divergence-free random drift that is of white-noise character. As already realized in the physics literature, […]

Speaker: Camillo De Lellis (Institute for Advanced Study) Consider a vector field v on the Euclidean space. The classical Cauchy-Lipschitz (also named Picard-Lindelöf) Theorem states that, if the vector field is Lipschitz in space, for every initial datum x there is a unique trajectory γ starting at x at time 0 and solving the ODE […]

Speaker: Camillo De Lellis (Institute for Advanced Study) After mentioning the fundamental theorems of DiPerna-Lions and Ambrosio on flows of Sobolev vector fields we will explore a number of sharpness questions related to them (a more detailed and elementary overview of the theorems and of the sharpness questions will already have been given in the […]