Propagation of regularity for solutions of the transport equation with non-Lipschitz velocity field and their applications

Prof. Quoc Hung Nguyen, Institute of Mathematical Sciences, Shanghaitech University

Since the work by Di Perna and Lions (’89) the continuity and transport equation under mild regularity assumptions on the vector field have been extensively studied, becoming a florid research field. 

The aim of this talk is to give an overview of the quantitative side of the theory, focusing mostly on the problem of propagation of regularity for ODE flows and solutions to the transport equation and the advection diffusion equation. We present recent results, examples, applications and open problems. This is based on joint works in collaboration with Elia Bruè.