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Serfati's approach to vortex patch problem

PDE and Applied Math Seminar

Speaker: Hantaek Bae, UC Davis
Location: 2112 MSB
Start time: Tue, May 20 2014, 4:10PM

Vortex patch is a solution of the 2D Euler equation with initial vorticity localized to a bounded region in the plane. Motivated by numerical results, Majda (1986) conjectured the possibility of loss of regularity of the boundary of patches (corners, or cusps, for instance) even if it is smooth initially. However, Chemin (1993) and Bertozzi-Constantin (1993) proved that loss of regularity of vortex-patch boundaries does not occur. In 1994, P. Serfati published a paper, a direct proof of global existence of 2D vortex patches. His result has the same generality as that of Chemin's, but he only outlined his proof. In this talk, I will provide details of his proof and will discuss possible applications of his idea. This is a joint work with James Kelliher (UC Riverside).