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SUMMARY:Vortex filament solutions of the 3D Navier-Stokes solutions - Jaco
 b Bedrossian (University of Maryland)
DTSTART:20220214T140000Z
DTEND:20220214T150000Z
UID:TALK170294@talks.cam.ac.uk
CONTACT:Daniel Boutros
DESCRIPTION:We consider solutions of the Navier-Stokes equations in 3d wit
 h vortex filament initial data of arbitrary circulation\, that is\, initia
 l vorticity given by a divergence-free\, vector-valued measure of arbitrar
 y mass supported on a smooth curve. First\, we prove global well-posedness
  for perturbations of the Oseen vortex column in scaling-critical spaces a
 t all circulation numbers. Second\, we prove local well-posedness (in a se
 nse to be made precise) when the filament is a smooth\, closed\, non-self-
 intersecting curve (again at all circulation numbers). Besides their physi
 cal interest\, these results are the first to give well-posedness in a nei
 ghborhood of large self-similar solutions of 3d Navier-Stokes\, as well as
  solutions which are locally approximately self-similar. In particular\, i
 n velocity form\, the initial condition is large in _BMO^-1_ \, a critical
  space in which local well-posedness of large data is unknown and conjectu
 red false (it is not in L^3 or weak L^3). Joint work with Pierre Germain a
 nd Ben Harrop-Griffiths 
LOCATION:CMS\, MR13
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