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CATEGORIES:Partial Differential Equations seminar
SUMMARY:Vortex filament solutions of the 3D Navier-Stokes
solutions - Jacob Bedrossian (University of Maryla
nd)
DTSTART;TZID=Europe/London:20220214T140000
DTEND;TZID=Europe/London:20220214T150000
UID:TALK170294AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/170294
DESCRIPTION:We consider solutions of the Navier-Stokes equatio
ns in 3d with vortex filament initial data of arbi
trary circulation\, that is\, initial vorticity gi
ven by a divergence-free\, vector-valued measure o
f arbitrary mass supported on a smooth curve. Firs
t\, we prove global well-posedness for perturbatio
ns of the Oseen vortex column in scaling-critical
spaces at all circulation numbers. Second\, we pro
ve local well-posedness (in a sense to be made pre
cise) when the filament is a smooth\, closed\, non
-self-intersecting curve (again at all circulation
numbers). Besides their physical interest\, these
results are the first to give well-posedness in a
neighborhood of large self-similar solutions of 3
d Navier-Stokes\, as well as solutions which are l
ocally approximately self-similar. In particular\,
in velocity form\, the initial condition is large
in _BMO^-1_ \, a critical space in which local we
ll-posedness of large data is unknown and conjectu
red false (it is not in L^3 or weak L^3). Joint wo
rk with Pierre Germain and Ben Harrop-Griffiths
LOCATION:CMS\, MR13
CONTACT:Daniel Boutros
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