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Mathematical Physics and Harmonic Analysis Seminar

Date: September 15, 2017

Time: 1:50PM - 2:50PM

Location: BLOC 628

Speaker: In-Jee Jeong, Princeton University


Title: Evolution of singular vortex patches

Abstract: A vortex patch is a solution to the 2D Euler equations whose vorticity is given by the characteristic function of a domain in the plane which evolves in time. In the 90s it was shown by Chemin, Bertozzi-Constantin, and Serfati that if the boundary of the domain is initially smooth (at least C^{1,\alpha} for \alpha > 0), then this smoothness propagates for all time. Much less is known for patches supported on domains with not so smooth boundaries, for example when the domain is initially a polygon. In this work, we show global well-posedness for vortex patches with corners when there is a certain rotational symmetry. We also prove some ill-posedness results in the absense of symmetries. This is joint work with Tarek M. Elgindi.