PDE Geometric Analysis seminar: Difference between revisions
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Abstract: The main goal of this talk is to discuss the classical (well known) versions of the strong maximum principle of Hopf and Oleinik, as well as the generalized maximum principle of Protter and Weinberger. These results serve as steps towards the theorem of characterization of the strong maximum principle of the speaker, Molina-Meyer and Amann, which substantially generalizes a popular result of Berestycki, Nirenberg and Varadhan. | Abstract: The main goal of this talk is to discuss the classical (well known) versions of the strong maximum principle of Hopf and Oleinik, as well as the generalized maximum principle of Protter and Weinberger. These results serve as steps towards the theorem of characterization of the strong maximum principle of the speaker, Molina-Meyer and Amann, which substantially generalizes a popular result of Berestycki, Nirenberg and Varadhan. | ||
===Changyou Wang=== | |||
Title: Some recent results on mathematical analysis of Ericksen-Leslie System | |||
Abstract: The Ericksen-Leslie system is the governing equation that describes the hydrodynamic evolution of nematic liquid crystal materials, first introduced by J. Ericksen and F. Leslie back in 1960's. It is a coupling system between the underlying fluid velocity field and the macroscopic average orientation field of the nematic liquid crystal molecules. Mathematically, this system couples the Navier-Stokes equation and the harmonic heat flow into the unit sphere. It is very challenging to analyze such a system by establishing the existence, uniqueness, and (partial) regularity of global (weak/large) solutions, with many basic questions to be further exploited. In this talk, I will report some results we obtained from the last few years. | |||
Revision as of 01:51, 30 August 2018
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 2019-Spring 2020
PDE GA Seminar Schedule Fall 2018-Spring 2019
| date | speaker | title | host(s) |
|---|---|---|---|
| August 31 (FRIDAY), | Julian Lopez-Gomez (Complutense University of Madrid) | The theorem of characterization of the Strong Maximum Principle | Rabinowitz |
| September 10, | Hiroyoshi Mitake (University of Tokyo) | TBA | Tran |
| September 17, | Changyou Wang (Purdue) | Some recent results on mathematical analysis of Ericksen-Leslie System | Tran |
| September 24/26, | Gunther Uhlmann (UWash) | TBA | Li |
| October 1, | Matthew Schrecker (UW) | TBA | Kim and Tran |
| October 8, | Anna Mazzucato (PSU) | TBA | Li and Kim |
| October 15, | Lei Wu (Lehigh) | TBA | Kim |
| October 22, | Annalaura Stingo (UCD) | TBA | Mihaela Ifrim |
| Time: TBD, | Jessica Lin (McGill University) | TBA | Tran |
| November 5, | Albert Ai (University of Berkeley) | TBA | Mihaela Ifrim |
| December 10, | ( ) | TBA | |
| January 28, | ( ) | TBA | |
| March 4 | Vladimir Sverak (Minnesota) | TBA(Wasow lecture) | Kim |
| March 18, | Spring recess (Mar 16-24, 2019) | ||
| April 29, | ( ) | TBA |
Abstracts
Julian Lopez-Gomez
Title: The theorem of characterization of the Strong Maximum Principle
Abstract: The main goal of this talk is to discuss the classical (well known) versions of the strong maximum principle of Hopf and Oleinik, as well as the generalized maximum principle of Protter and Weinberger. These results serve as steps towards the theorem of characterization of the strong maximum principle of the speaker, Molina-Meyer and Amann, which substantially generalizes a popular result of Berestycki, Nirenberg and Varadhan.
Changyou Wang
Title: Some recent results on mathematical analysis of Ericksen-Leslie System
Abstract: The Ericksen-Leslie system is the governing equation that describes the hydrodynamic evolution of nematic liquid crystal materials, first introduced by J. Ericksen and F. Leslie back in 1960's. It is a coupling system between the underlying fluid velocity field and the macroscopic average orientation field of the nematic liquid crystal molecules. Mathematically, this system couples the Navier-Stokes equation and the harmonic heat flow into the unit sphere. It is very challenging to analyze such a system by establishing the existence, uniqueness, and (partial) regularity of global (weak/large) solutions, with many basic questions to be further exploited. In this talk, I will report some results we obtained from the last few years.