Gianluca Crippa (Scuola Normale Superiore, Pisa)

Ordinary differential equations with non-Lipschitz vector field

In this talk I will survey some recent literature about the transport equation 
and the ordinary differential equation with non-Lipschitz vector field. In the 
first part I will describe the ``abstract'' connection between these two 
problems. In the second part I will present some recent results, obtained in 
collaboration with Camillo De Lellis, which consist in a purely Lagrangian 
study of the ordinary differential equation, via some elementary integral 
estimates on the flow. These estimates not only allow to recover some old 
results in a simple and direct way, but they also have some new corollaries.