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On the limiting behaviour of regularizations<br/><br/>of the Euler Equations with vortex sheet initial data<br/><br/>

Monday, February 22, 2010 - 11:30am - 12:15pm
EE/CS 3-180
Monika Nitsche (University of New Mexico)
Keywords: vortex sheet motion, vortex blob method, Euler-alpha model

Abstract: The vortex sheet is a mathematical model for a shear layer
in which the layer is approximated by a surface. Vortex
sheet evolution has been shown to approximate the motion
of shear layers well, both in the case of free layers and
of separated flows at sharp edges.
Generally, the evolving sheets develop singularities
in finite time. To approximate the fluid past this time,
the motion is regularized and the sheet defined as the
limit of zero regularization. However, besides weak existence
results in special cases, very little is
known about this limit. In particular, it is not known whether
the limit is unique or whether it depends on the regularization.

I will discuss several regularizing mechanisms, including physical
ones such as fluid viscosity, and purely numerical ones such
as the vortex blob and the Euler-alpha methods. I will show
results for a model problem and discuss some of the unanswered
questions of interest.
MSC Code: 
76M23
Keywords: