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DTSTART;TZID=America/Los_Angeles:20260209T161500
DTEND;TZID=America/Los_Angeles:20260209T171500
DTSTAMP:20260520T005939
CREATED:20260205T210218Z
LAST-MODIFIED:20260205T210218Z
UID:3983-1770653700-1770657300@colleges.claremont.edu
SUMMARY:A BKM-type criterion for the 3D incompressible Euler equations (Mustafa Aydin\, USC)
DESCRIPTION:Abstract: The three-dimensional incompressible Euler equations describe the motion of an ideal fluid\, yet the mechanisms that govern the possible loss of regularity of smooth solutions remain only partially understood. A classical result of Beale\, Kato\, and Majda shows that if a smooth solution breaks down in finite time\, then the time integral of the vorticity’s supremum norm must diverge\, providing a sharp conditional criterion for regularity. \nIn this talk\, I will present a new blow-up criterion in the spirit of the Beale–Kato–Majda theorem that emphasizes a different form of control. Instead of requiring bounds on the full vorticity\, the criterion involves tangential derivatives of the velocity field\, and shows that smooth solutions persist as long as these derivatives remain appropriately bounded in time. The result holds in a variety of settings\, including the whole space\, periodic domains\, and domains with boundaries.
URL:https://colleges.claremont.edu/ccms/event/a-bkm-type-criterion-for-the-3d-incompressible-euler-equations-mustafa-aydin-usc/
LOCATION:Emmy Noether Room\, Estella 1021\, Pomona College\,\, 610 N. College Ave.\, Claremont\, CA\, 91711\, United States
CATEGORIES:Analysis Seminar
ORGANIZER;CN="Ryan Aschoff":MAILTO:ryan.aschoff@cgu.edu
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DTSTART;TZID=America/Los_Angeles:20260212T161500
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DTSTAMP:20260520T005939
CREATED:20260207T012748Z
LAST-MODIFIED:20260207T014348Z
UID:3984-1770912900-1770916500@colleges.claremont.edu
SUMMARY:Analysis Seminar: Generalized Elmendorf’s Theorem in Context (Sofía Martínez Alberga\, Bryn Mawr College)
DESCRIPTION:Abstract: In general\, the objective of algebraic topology is to classify spaces using some algebraic invariants or up to some notion of equivalence. In the area of equivariant homotopy theory\, the goal is the same but now spaces equipped with a group action are considered and algebraic invariants of choice are homotopy groups. It turns out there is an analogous version of Whitehead’s theorem in the equivariant setting which in some sense motivates studying weak homotopy equivalences over homotopy equivalences. This talk will review some of these homotopical notions and introduce Elmendorf’s theorem. Proved in the eighties\, this theorem sheds some light on how one can better understand equivariant homotopical notions as functors from the orbit category of the group to the category of topological spaces. Also\, in this talk we will address how this perspective is used more modernly to understand better equivariant notions of other categories and to expand nonequivariant notions to equivariant ones.
URL:https://colleges.claremont.edu/ccms/event/analysis-seminar-generalized-elmendorfs-theorem-in-context-sofia-martinez-alberga-bryn-mawr-college/
LOCATION:Estella 2099\, Pomona College\, 610 N. College Ave.\, Claremont\, CA\, United States
CATEGORIES:Analysis Seminar
ORGANIZER;CN="Asuman Aksoy":MAILTO:asuman.aksoy@claremontmckenna.edu
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