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 - Wasow lecture	Benoit Perthame (University of Paris VI)		Jin
February 13	Bing Wang (UW)	The extension problem of the mean curvature flow	Kim & Tran
February 20	Eric Baer (UW)	Isoperimetric sets inside almost-convex cones	Kim & Tran
February 27	Ben Seeger (University of Chicago)	Homogenization of pathwise Hamilton-Jacobi equations	Tran
March 7 - Mathematics Department Distinguished Lecture	Roger Temam (Indiana University)	On the mathematical modeling of the humid atmosphere	Smith
March 8 - Analysis/Applied math/PDE seminar	Roger Temam (Indiana University)	Weak solutions of the Shigesada-Kawasaki-Teramoto system	Smith
March 13	Sona Akopian (UT-Austin)		Kim
March 27 - Analysis/PDE seminar	Sylvia Serfaty (Courant)		Tran
March 29 - Wasow lecture	Sylvia Serfaty (Courant)
April 3	Zhenfu Wang (Maryland)		Kim
April 10	Andrei Tarfulea (Chicago)	Improved estimates for thermal fluid equations	Baer
April 17	Siao-Hao Guo (Rutgers)	TBA	Lu Wang
April 24	Jianfeng Lu	TBA	Li
April 25- joint Analysis/PDE seminar	Chris Henderson (Chicago)	TBA	Lin
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.

Bing Wang

We show that the mean curvature blows up at the first finite singular time for a closed smooth embedded mean curvature flow in R3. This is a joint work with H.Z. Li.

Eric Baer

We discuss a recent result showing that a characterization of isoperimetric sets (that is, sets minimizing a relative perimeter functional with respect to a fixed volume constraint) inside convex cones as sections of balls centered at the origin (originally due to P.L. Lions and F. Pacella) remains valid for a class of "almost-convex" cones. Key tools include compactness arguments and the use of classically known sharp characterizations of lower bounds for the first nonzero Neumann eigenvalue associated to (geodesically) convex domains in the hemisphere. The work we describe is joint with A. Figalli.

Ben Seeger

I present a homogenization result for pathwise Hamilton-Jacobi equations with "rough" multiplicative driving signals. In doing so, I derive a new well-posedness result when the Hamiltonian is smooth, convex, and positively homogenous. I also demonstrate that equations involving multiple driving signals may homogenize or exhibit blow-up.

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.