
08/30 09:00am 
Zoom 
Tak Kwong Wong University of Hong Kong 
Regularity structure, globalintime wellposedness and longtime behavior of energy conservative solutions to the HunterSaxton equation
The HunterSaxton equation is an integrable equation in one spatial dimension, and can be used to study the nonlinear instability in the director field of a nematic liquid. In this talk, we will discuss the regularity structure, globalintime wellposedness and longtime behavior of energy conservative solutions to the HunterSaxton equation. In particular, singularities for the energy measure may only appear at at most countably many times, and are completely determined by the absolutely continuous part of initial energy measure. The temporal and spatial locations of singularities are explicitly determined by the initial data as well. The longtime behavior of energy conservative solution is given by a kinkwave that is determined by the total energy of the system only. The analysis is based on using the method of characteristics in a generalized framework that consists of the evolutions of energy conservative solution and its energy measure. This is a joint work with Yu Gao and Hao Liu. 

09/13 3:00pm 
BLOC 302 
Edriss S. Titi Texas A&M University and University of Cambridge 
Mathematical Analysis of Atmospheric and Oceanic Dynamics Models: Cloud Formation and Seaice Models
In this talk we will present rigorous analytical results concerning global regularity, in the viscous case, and finitetime singularity, in the inviscid case, for oceanic and atmospheric dynamics models. Moreover, we will also provide a rigorous justification of the derivation of the Primitive Equations of planetary scale oceanic dynamics from the threedimensional NavierStokes equations as the vanishing limit of the small aspect ratio of the depth to horizontal width. In addition, we will also show the global wellposedeness of the coupled threedimensional viscous Primitive Equations with a microphysics phase change moisture model for cloud formation. Eventually, we will also present shorttime wellposedness of solutions to the Hibler’s seaice model. 