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SUMMARY:Initial Value Problem and Vortex Sheets: Analysis and Computation 
 - Ambrose\, D (Drexel University)
DTSTART:20140806T090000Z
DTEND:20140806T113000Z
UID:TALK53669@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:In this lecture\, we will discuss the irrotational water wave 
 problem. We will place the problem in the larger context of vortex sheets\
 ; the vortex sheet is the interface between two irrotational fluids\, allo
 wing for a jump in the tangential components of velocity across the interf
 ace. We will present the equations of motion in both 2D and 3D\, for the w
 ater wave problem both with and without surface tension. We will present t
 he numerical method of Hou\, Lowengrub\, and Shelley (HLS) for computing s
 olutions of the initial value problem in 2D\, and how the HLS ideas can be
  used to prove short-time well-posedness of the initial value problem. The
  corresponding numerical method and well-posedness proofs for the three-di
 mensional problem will also be discussed. If time allows\, we will go beyo
 nd the initial value problem\, and discuss how the vortex sheet formulatio
 n with the HLS ideas can be extended to treat other problems\, such as the
  traveling wave problem. This talk includes joint work with Nader Masmoudi
 \, Michael Siegel\, Svetlana Tlupova\, and possibly others.\n\n
LOCATION:CMS\, RM9
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