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CATEGORIES:Cambridge Analysts' Knowledge Exchange
SUMMARY:Vortex Patch Solutions of the 2D Euler Equations -
Martin Taylor
DTSTART;TZID=Europe/London:20120307T160000
DTEND;TZID=Europe/London:20120307T173000
UID:TALK36205AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/36205
DESCRIPTION:The Euler equations govern the flow of incompressi
ble inviscid fluids. In two dimensions the vortic
ity (the curl of the velocity vector field) is pre
served along particle trajectories. The talk will
focus on a special class of weak solutions\, call
ed vortex patches\, where the initial vorticity is
the indicator function of some bounded simply con
nected region. Since vorticity is preserved\, the
solution will remain an indicator of some bounded
simply connected region\, with the \nregion evolv
ing in time.\n\nAfter reviewing some basic notions
such as particle trajectory maps and the vorticit
y stream formulation\, we define a suitable weak f
ormulation in order to be able to discuss such sol
utions. We will then sketch an argument to show t
hat if the boundary of the vortex patch is initial
ly sufficiently smooth\, it will remain smooth glo
bally in time.\n
LOCATION:MR14\, CMS
CONTACT:Edward Mottram
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