学术报告 报告题目一：Regularity of Solutions for Some Degenerate Equations
报 告 人：陈化 教授 （武汉大学）
报告时间：2016年6月10日（星期五）上午09:30-10:30
报告题目二：Global Stability of Hydrostatic Equilibria Associated With Buoyancy Driven Fluid Flows
报 告 人：赵坤 教授（杜兰大学）
报告时间：2016年6月10日（星期五）上午10:30-11:30
报告地点：4号楼4318室
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数学学院
2016年06月06日
报告一摘要：
In this talk, I would report some results on the Gevrey (or analytic) regularities of solutions for some degenerate partial differential equations, which including (1) generalized Kolmogorov equations（or linear Boltzmann equations), (2) Fokker-Planck equations,(3) Landau equations and (4) sub-elliptic Monge-Ampere equations.
报告二摘要：
The two-dimensional Navier-Stokes-Boussinesq (NSB) system (derived by Joseph Valentin Boussinesq around 1897) is frequently used in fluid dynamics modeling buoyancy driven fluid flows, as well as other situations in astrophysics, and atmospheric and oceanographic sciences where stratification and rotation play a dominant role. Mathematically, the 2D NSB is also well-known, due to its close connection with classical models in mathematical fluid dynamics, such as the incompressible Navier-Stokes/Euler equations. In this talk, I will briefly introduce the background of the model, and report some recent progress regarding rigorous and numerical studies conducted on the model. In particular, I will introduce results concerning the long-time asymptotic behavior of strong solutions to the model on 2D bounded domains with physical boundaries subject to various types of physically relevant and computationally effective boundary conditions, which is related to demonstrating the global stability of hydrostatic equilibria associated with buoyancy driven fluid flows. This is a joint work with Charles Doering (University of Michigan - Ann Arbor), Jiahong Wu (Oklahoma State University) and Xiaoming Zheng (Central Michigan University).