PDE Geometric Analysis seminar: Difference between revisions
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Revision as of 20:22, 6 February 2017
The seminar will be held in room 901 of Van Vleck Hall on Mondays from 3:30pm - 4:30pm, unless indicated otherwise.
Previous PDE/GA seminars
Tentative schedule for Fall 2017
PDE GA Seminar Schedule Spring 2017
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||[[ ]]|
|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|
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.
We consider the patch evolution under the 2D Euler dynamics and study how the geometry of the boundary can deteriorate in time.
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.
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.