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Center for Scientific Computation and Mathematical Modeling

Research Activities > Programs > Incompressible Flows at High Reynolds Number > Helena Lopes

Analytical and Computational Challenges of Incompressible Flows at High Reynolds Number

CSIC Building (#406), Seminar Room 4122.
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On vortex sheet evolution

Dr. Helena Lopes

Mathematics Department at Pennsylvania State University

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.