报告题目： The incompressible Navier-Stokes equations in vacuum
时间地点: 11月12日下午4:00-5:00 后主楼1124
报告人: Professor Piotr Boguslaw Mucha (University of Warsaw, Poland)
摘要：We are concerned with the existence and uniqueness issue for the inhomogeneous incompressible Navier-Stokes equations supplemented with H^1 initial velocity and only bounded nonnegative density. In contrast with all the previous works on that topics, we do not require regularity or positive lower bound for the initial density, or compatibility conditions for the initial velocity, and still obtain unique solutions. Those solutions are global in the two-dimensional case for general data, and in the three-dimensional case if the velocity satisfies a suitable scaling invariant smallness condition. As a straightforward application, we provide a complete answer to Lions' question concerning the evolution of a drop of incompressible viscous fluid in the vacuum.
The talk will base on the joint result with Raphael Danchin, arXiv:1705.06061 [math.AP] (to appear in CPAM).