Mathematics

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 applicability of this theory is very wide, especially in the study of partial differential equations and very recently also in the field of non-smooth geometry.

The aim of this talk is to give an overview of the quantitative side of the theory initiated by Crippa and De Lellis. We present sharp regularity estimates under various assumptions on the velocity field.

Eventually we discuss an application to the 2D Euler equation.

This is a joint work with Quoc-Hung Nguyen.