Special Session 7: 

A drop of water

Piotr Mucha
University of Warsaw
I will talk about the issue of existence and uniqueness of solution to the Inhomogeneous Navier-Stokes system (INS) in a two dimensional domain. The key point it that the initial density can be just a characteristic function of a set. Even for such rough solutions the result provides unique solutions. As a historical remark, it is emphasized that it solves the problem put by PL Lions in his book concerning weak solutions to INS. The talk will be based on joint results with Raphael Danchin (Paris). Preprint: https://arxiv.org/abs/1705.06061