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...
摘要:This is an summary talk for Moser-Trudinger inequality. In this talk, I first introduce the classical Moser-Trudinger inequalities in bounded domain and unbounded domain. Then I will present the work on the existence and no-existence for extremals of Moser-Trudinger inequality. The Trace-type Moser-Trudinger inequality in bounded and unbounded domain will be also discussed in this talk. F...