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SUMMARY:Blow-up of arbitrarily rough critical Besov norms at any Navier-St
 okes singularity - Gabriel Koch (University of Sussex)
DTSTART:20131028T150000Z
DTEND:20131028T160000Z
UID:TALK46866@talks.cam.ac.uk
CONTACT:25129
DESCRIPTION:We show that the spatial norm in any critical homogeneous Beso
 v space in which local existence of strong solutions to the 3-d Navier-Sto
 kes equations is known must become unbounded near a singularity. In partic
 ular\, the regularity of these spaces can be arbitrarily close to -1\, whi
 ch is the lowest regularity of any Navier-Stokes critical space. This exte
 nds a well-known result of Escauriaza-Seregin-Sverak (2003) concerning the
  Lebesgue space L^3\, a critical space with regularity 0 which is continuo
 usly embedded into the spaces we consider.  We follow the "critical elemen
 t" reductio ad absurdum method of Kenig-Merle based on profile decompositi
 ons\, but due to the low regularity of the spaces considered we rely on an
  iterative algorithm to improve low-regularity bounds on solutions to boun
 ds on a part of the solution in spaces with positive regularity.  This is 
 joint work with I. Gallagher (Paris 7) and F. Planchon (Nice).
LOCATION:CMS\, MR13
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