中国科学院数学与系统科学研究院

科研进展与学术交流报告会

（第116期）

报告人：Emmanuel Grenier 教授（北京理工大学）

题  目：Boundary layers of Navier-Stokes equations

摘 要：Boundary layers appear when the viscosity of the fluid goes to zero. They play a crucial role in the stability of the overall flow and in particular the onset of turbulence. They have been intensively studied in physics in the 20th century, starting with L. Prandtl in 1904, who was followed by Orr, Sommerfeld, Tollmien, Schlichting, C.C. Lin, amongst many others. Their mathematical study is however much more recent. After a general presentation of boundary layers, I will introduce recent results on the spectral theory of the Orr-Sommerfeld equation, on the use of generator functions to get a simple proof of the classical Cauchy Kovalevskaya theorem,  on the use of holomorphic functions to build nonlinear instabilities and on the localization of instabilities  to get multi-layers instabilities. In particular I will show that every boundary layer of the Navier-Stokes equations is linearly and non-linearly unstable provided the viscosity is small enough and discuss how Prandtl's layer Ansatz breaks down for initial data with Sobolev regularity and how very complex and previously non described flows appear.

时  间：2025.9.5(星期五), 10:40-11:50

地  点：南楼204会议室