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SUMMARY:Vortex Patch Solutions of the 2D Euler Equations - Martin Taylor
DTSTART:20120307T160000Z
DTEND:20120307T173000Z
UID:TALK36205@talks.cam.ac.uk
CONTACT:Edward Mottram
DESCRIPTION:The Euler equations govern the flow of incompressible inviscid
  fluids.  In two dimensions the vorticity (the curl of the velocity vector
  field) is preserved along particle trajectories.  The talk will focus on 
 a special class of weak solutions\, called vortex patches\, where the init
 ial vorticity is the indicator function of some bounded simply connected r
 egion.  Since vorticity is preserved\, the solution will remain an indicat
 or of some bounded simply connected region\, with the \nregion evolving in
  time.\n\nAfter reviewing some basic notions such as particle trajectory m
 aps and the vorticity stream formulation\, we define a suitable weak formu
 lation in order to be able to discuss such solutions.  We will then sketch
  an argument to show that if the boundary of the vortex patch is initially
  sufficiently smooth\, it will remain smooth globally in time.\n
LOCATION:MR14\, CMS
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