BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Talks.cam//talks.cam.ac.uk//
X-WR-CALNAME:Talks.cam
BEGIN:VEVENT
SUMMARY:Non-uniqueness of Leray solutions of the forced Navier-Stokes equa
 tions - Maria Colombo (EPFL - Ecole Polytechnique Fédérale de Lausanne)
DTSTART:20220215T111500Z
DTEND:20220215T121500Z
UID:TALK167387@talks.cam.ac.uk
DESCRIPTION:In his seminal work\, Leray demonstrated the existence of glob
 al weak solutions\, with nonincreasing energy\, to the Navier-Stokes equat
 ions in three dimensions. In this talk we exhibit two distinct Leray solut
 ions with zero initial velocity and identical body force.&nbsp\;\nThe star
 ting point of our construction is Vishik's answer to another long-standing
  problem in fluid dynamics\, namely whether the Yudovich uniqueness result
  for the 2D Euler system can be extended to the class of L^p-integrable vo
 rticity. Building on Vishik's work\, we construct a `background' solution 
 which is unstable for the 3D Navier-Stokes dynamics\; the second solution 
 from the same initial datum is a trajectory on the unstable manifold assoc
 iated to the background solution\, in accordance with the predictions of J
 ia and &Scaron\;ver&aacute\;k.
LOCATION:Seminar Room 1\, Newton Institute
END:VEVENT
END:VCALENDAR