Title1:Regularity of Solutions for Some Degenerate Equations

Time: Fri, June 10, 2016, AM 09:30-10:30

Speaker:Prof. Hua Chen （ Wuhan University）

Title2:Global Stability of Hydrostatic Equilibria Associated With Buoyancy Driven Fluid Flows

Time: Fri, June 10, 2016, AM 10:30-11:30

Speaker:Prof.Kun Zhao （ Tulane University）

Location:Room 4318, Building No.4, Wushan Campus

Abstract1: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. 

Abstract2: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).