學術活動
PDEs in a tea cup
2009-06-30
來源：科技處 點擊次數：主講人： Professor Ronghua Pan（Georgia Institute of Technology）
时 间：7月3日（星期五）下昼16：00-17：00
地 点： 數學科學學院412 课堂
主 办： 數學科學學院
摘 要： The motion of the fluid in a tea-cup on a desk can be modeled by the viscous Boussinesq's system in a 2D compact domain. Under the dissipation of viscosity and the non-slip boundary condition, the fluid is observed to tend the stable asymptotic where the velocity is zero and the density distributed as a monotone function of the depth due the effect of gravity. Mathematically, such a system is commonly used approximation to 3D incompressible fluid dynamics, sharing the key difficulty of vortex stretching. We prove the global regularity of the problem for smooth initial data. Some information on the asymptotics is also proved.This is a joint work with M. Lai and K. Zhao.
