BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//talks.cam.ac.uk//v3//EN
BEGIN:VTIMEZONE
TZID:Europe/London
BEGIN:DAYLIGHT
TZOFFSETFROM:+0000
TZOFFSETTO:+0100
TZNAME:BST
DTSTART:19700329T010000
RRULE:FREQ=YEARLY;BYMONTH=3;BYDAY=-1SU
END:DAYLIGHT
BEGIN:STANDARD
TZOFFSETFROM:+0100
TZOFFSETTO:+0000
TZNAME:GMT
DTSTART:19701025T020000
RRULE:FREQ=YEARLY;BYMONTH=10;BYDAY=-1SU
END:STANDARD
END:VTIMEZONE
BEGIN:VEVENT
CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:On the 2-point problem for the Lagrange-Euler equa
 tion - Shnirelman\, A (Concordia University\, Cana
 da)
DTSTART;TZID=Europe/London:20120828T113000
DTEND;TZID=Europe/London:20120828T123000
UID:TALK39419AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/39419
DESCRIPTION:Consider the motion of ideal incompressible fluid 
 in a bounded domain (or on a compact Riemannian ma
 nifold). The configuration space of the fluid is t
 he group of volume-preserving diffeomorphisms of t
 he flow domain\, and the flows are geodesics on th
 is infinite-dimensional group where the metric is 
 defined by the kinetic energy. The geodesic equati
 on is the Lagrange-Euler equation.\nThe problem us
 ually studied is the initial-value problem\, where
  we look for a geodesic with given initial fluid c
 onfiguration and initial velocity field. In this t
 alk we consider a different problem: find a geodes
 ic connecting two given fluid configurations. The 
 main result is the following\nTheorem: Suppose the
  flow domain is a 2-dimensional torus. Then for an
 y two fluid configurations there exists a geodesic
  connecting them. This means that\, given arbitrar
 y fluid configuration (diffeomorphism)\, we can "p
 ush"\nthe fluid along some initial velocity field\
 , so that by time one the fluid\, moving according
  to the Lagrange- Euler equation\, assumes the giv
 en configuration. This theorem looks superficially
  like the Hopf-Rinow theorem for finite-dimensiona
 l Riemannian manifolds. In fact\, these two theore
 ms have almost nothing in common.\nIn our case\, u
 nlike the Hopf-Rinow theorem\, the geodesic is not
 \, in general case\, the shortest curve connecting
  the endpoints (fluid configurations).\nMoreover\,
  the length minimizing curve can not exist at all\
 , while the geodesic always exists. The proof is b
 ased on some ideas of global analysis (Fredholm qu
 asilinear maps) and microlocal analysis of the Lag
 range-Euler equation (which may be called a ?micro
 global analysis?).\n\n
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:Mustapha Amrani
END:VEVENT
END:VCALENDAR