Abstract:Whether the 3D incompressible Euler equations can develop a finite time singularity from smooth initial data is one of the most challenging problems in nonlinear PDEs. In this talk, we will present a new exciting result with Dr. Jiajie Chen in which we prove finite time blowup of the 2D Boussinesq and 3D Euler equations with smooth initial data and boundary. There are several essentia...
Record: YesLevel: Graduate & UndergraduateLanguage: EnglishPrerequisite:Differential Geometry, Riemannian GeometryIntroduction:Black holes play a central role in general relativity and astrophysics. The Kerr solution of the Einstein equations describes a spacetime containing an isolated, rotating black hole. Following a brief introduction to the Cauchy problem for the Einstein equations, I will...