CANCELED – Transport equations and anomalous dissipation

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 previous lecture, but anyway this seminar will be arranged so that it can be followed independently from the latter). Many of these questions have been at least partially answered in the last few years and I will first survey what is the overall understanding which we have gained on them. I will then focus on a particular one and highlight its link with a phenomenon which is poorly understood at the rigorous mathematical level: the occurrence of the so-called anomalous dissipation in incompressible fluid dynamics.

This lecture is preceded by a mini-course on Flows of nonsmooth vector fields.