Max von Renesse
Title: Strong Feller Regularization for 1D Nonlinear Transport by Reflected Ornstein Uhlenbeck Noise
Abstract
We consider equations of nonlinear transport on the circle with regular self interactions appearing in aggregation models and deterministic mean field dynamics. We introduce a random perturbation of such systems through a stochastic orientation preserving flow, which is given as an integrated infinite dimensional periodic Ornstein- Uhlenbeck process with reflection. As our main result we show that the induced stochastic dynamics yields a measure valued Markov process on a class of regular measures. Moreover, we show that this process is strong Feller in the corresponding topology. This is interpreted as a qualitative regularisation by noise phenomenon.
Joint work with Feng-Yu Wang (Tianjin) and Alexander Weiss (Leipzig)