PDE Geometric Analysis seminar

The seminar will be held in room 901 of Van Vleck Hall on Mondays from 3:30pm - 4:30pm, unless indicated otherwise.

PDE GA Seminar Schedule Spring 2017

date	speaker	title	host(s)
January 23 Special time and location: 3-3:50pm, B325 Van Vleck	Sigurd Angenent (UW)	Ancient convex solutions to Mean Curvature Flow	Kim & Tran
January 30	Serguei Denissov (UW)	Instability in 2D Euler equation of incompressible inviscid fluid	Kim & Tran
February 6	Benoit Perthame (University of Paris VI)		Wasow lecture
February 13	Bing Wang (UW)	The extension problem of the mean curvature flow	Kim & Tran
February 20	Hans-Joachim Hein (Fordham)		Viaclovsky
February 27	Ben Seeger (University of Chicago)		Tran
March 7 - Applied math/PDE/Analysis seminar	Roger Temam (Indiana University)		Mathematics Department Distinguished Lecture
March 8 - Applied math/PDE/Analysis seminar	Roger Temam (Indiana University)		Mathematics Department Distinguished Lecture
March 13	Sona Akopian (UT-Austin)		Kim
March 27 - Analysis/PDE seminar	Sylvia Serfaty (Courant)		Tran
March 29	Sylvia Serfaty (Courant)		Wasow lecture
April 3	Zhenfu Wang (Maryland)		Kim
April 10	Andrei Tarfulea (Chicago)	Improved estimates for thermal fluid equations	Baer
May 1st	Jeffrey Streets (UC-Irvine)		Bing Wang

Abstracts

Sigurd Angenent

The Huisken-Hamilton-Gage theorem on compact convex solutions to MCF shows that in forward time all solutions do the same thing, namely, they shrink to a point and become round as they do so. Even though MCF is ill-posed in backward time there do exist solutions that are defined for all t<0 , and one can try to classify all such “Ancient Solutions.” In doing so one finds that there is interesting dynamics associated to ancient solutions. I will discuss what is currently known about these solutions. Some of the talk is based on joint work with Sesum and Daskalopoulos.

Serguei Denissov

We consider the patch evolution under the 2D Euler dynamics and study how the geometry of the boundary can deteriorate in time.

Andrei Tarfulea

We consider a model for three-dimensional fluid flow on the torus that also keeps track of the local temperature. The momentum equation is the same as for Navier-Stokes, however the kinematic viscosity grows as a function of the local temperature. The temperature is, in turn, fed by the local dissipation of kinetic energy. Intuitively, this leads to a mechanism whereby turbulent regions increase their local viscosity and dissipate faster. We prove a strong a priori bound (that would fall within the Ladyzhenskaya-Prodi-Serrin criterion for ordinary Navier-Stokes) on the thermally weighted enstrophy for classical solutions to the coupled system.