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Abstract:
Vortex sheets (in two dimensions) are curves along which the tangential
component of velocity is discontinuous, while the normal component is
continuous. One instance where vortex sheets arise is the (idealized) flow
trailing an airplane wing. The evolution of vortex sheets has been modeled in
two different ways: as solutions of the Birkhoff-Rott equation or as weak
solutions of the incompressible 2D Euler equations with vortex sheet initial
data. In this talk we explore a few issues which have arisen as a result of
recent progress, namely, ill-posedness of the Birkhoff-Rott equations;
existence, uniqueness and nonuniqueness of weak solutions of 2D Euler, and the
relation between the two models.
[LECTURE SLIDES]
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