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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Non-uniqueness of Leray solutions of the forced Na
vier-Stokes equations - Maria Colombo (EPFL - Ecol
e Polytechnique Fédérale de Lausanne)
DTSTART;TZID=Europe/London:20220215T111500
DTEND;TZID=Europe/London:20220215T121500
UID:TALK167387AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/167387
DESCRIPTION:In his seminal work\, Leray demonstrated the exist
ence of global weak solutions\, with nonincreasing
energy\, to the Navier-Stokes equations in three
dimensions. In this talk we exhibit two distinct L
eray solutions with zero initial velocity and iden
tical body force. \;\nThe starting point of ou
r construction is Vishik's answer to another long-
standing problem in fluid dynamics\, namely whethe
r the Yudovich uniqueness result for the 2D Euler
system can be extended to the class of L^p-integra
ble vorticity. Building on Vishik's work\, we cons
truct a `background' solution which is unstable fo
r the 3D Navier-Stokes dynamics\; the second solut
ion from the same initial datum is a trajectory on
the unstable manifold associated to the backgroun
d solution\, in accordance with the predictions of
Jia and &Scaron\;verá\;k.
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:
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