[Turkmath:4942] İ.Ü. Matematik Bölüm Semineri

[TEMHA ERKOÇ YILMAZTÜRK]

Merhabalar,

16.06.2021 tarihinde  saat 15:00 te  Louisiana State  Üniversitesinden Dr.
Öğr. Üyesi  Aynur Bulut  başlık ve özeti aşağıda verilen bir konuşma
yapacaktır. Seminer Zoom programı üzerinden online yapılacaktır. Katılmak
isteyenlerin katılım bilgilerini alabilmeleri için "
huseyinuysal at istanbul.edu.tr "  adresine mail atmaları gerekmektedir.


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*Başlık:*Recent Developments in Energy Supercritical Problems for Nonlinear
Dispersive Partial Differential Equations

*Özet:* The question of global existence for solutions to the defocusing
energy-supercritical nonlinear dispersive equations and wave equations such
as the nonlinear Schrodinger and nonlinear wave equation has been a
longstanding open question, often thought of as a model problem related to
understanding the role of supercritical scaling in the equations of fluid
mechanics.
In this talk, I will give an introduction to these PDEs and an overview of
what is known about the energy supercritical setting. This will touch on
concentration compactness techniques, from which it is by now
well-understood that uniform control in the scaling-critical L^2-based
homogeneous Sobolev norm prevents finite-time blowup (and indeed implies a
scattering result), as well as recent results concerning a construction of
finite-time blow up for solutions evolving from certain smooth data due to
Merle, et al., and connections with recent work based on a quantitative
version (i.e. not based on compactness arguments) of the
uniform-critical-control implies scattering results.  The talk will be
self-contained and accessible to graduate students from a variety of areas.

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İyi günler dileğiyle,

Temha

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