报告题目：Global-in-time regularity of the two-dimensional incompressible Navier-Stokes equations with variable viscosity coefficient

报 告 人：廖娴 教授 （卡尔斯鲁厄理工大学）

报告时间：2025年3月10日（星期一）14:30- 15:30

报告地点：新浦金350vip一114      

报告摘要：In this talk, we investigate the global-in-time regularity of the two-dimensional incompressible Navier-Stokes equations in the presence of large variations in the viscosity coefficient. Through the analysis of a hidden fourth-order elliptic operator applied to the stream function, both globally and locally, we establish the Lipschitz continuity of the velocity field, even when its normal derivative exhibits discontinuities across viscosity-interfaces. Specifically, we demonstrate that the two-phase two-dimensional Navier-Stokes equations admit a unique global-in-time solution that maintains the regularity of the free interface. This is joint work with Rebekka Zimmermann.

报告人简介：廖娴，2018年至今在德国卡尔斯鲁厄理工大学担任青年教授。2004年至2009年在南京大学学习，2013年博士毕业于巴黎东大学，之后在捷克查尔斯大学，中国科学院数学与系统科学研究院以及德国波恩大学从事博士后研究。研究兴趣为偏微分方程，流体力学，可积系统，自由界面问题，非线性色散方程等。