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SUMMARY:Applications of Arnold's variational principle to the stability of
  vortices in ideal and viscous flows - Thierry Gallay (Université Grenobl
 e Alpes)
DTSTART:20220216T094500Z
DTEND:20220216T104500Z
UID:TALK167396@talks.cam.ac.uk
DESCRIPTION:We revisit Arnold's variational approach to the stability of s
 teady-state solutions of the two-dimensional Euler equations. In thecase o
 f planar vortices\, we study in detail the quadratic form that represents 
 the second variation of the energy on the isovorticalsurface. We show in p
 articular that\, for a large class of radially symmetric vortices with str
 ictly decreasing profile\, the secondvariation is negative definite for al
 l perturbations that preserve the total circulation. We use that property 
 to give a new stabilityproof for the Oseen vortex as a self-similar soluti
 on of the 2D Navier-Stokes equations\, and to investigate the vanishing vi
 scositylimit of axisymmetric vortex rings. This talk is based on joint wor
 k with V. Sverak.
LOCATION:Seminar Room 1\, Newton Institute
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