分析和PDE讨论班——The incompressible Navier-Stokes equations with vacuum
主 题: 分析和PDE讨论班——The incompressible Navier-Stokes equations with vacuum
报告人: Raphael Danchin (Universite Paris-Est)
时 间: 2017-10-17 16:00-17:00
地 点: 理科1号楼1114
Abstract: 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(we do not require regularity or positive lower bound, or compatibility conditions for the initial velocity). We prove global existence and uniqueness for general two-dimensional data, and in the three-dimensional case, if the velocity satisfies a suitable scaling invariant smallness condition. As an application, we solve a question raised by P.-L. Lions concerning the evolution of a drop of incompressible viscous liquid in the vacuum.
This is a joint work with Piotr B. Mucha.