[11.03]Vortex Patches of Serfati
- 수학전공
- 조회수2122
- 2016-11-02
▣ 연 사 : 배한택 교수(UNIST)
▣ 일 시 : 2016년 11월 3일(목) 4:30 - 5:30
▣ 장 소 : 31316호(수학과 전공강의실)
▣ 대 상 : 수학과 학부생 및 대학원생
▣ 다 과 : 4시 20분부터
Abstract
In 1993, two proofs of the persistence of regularity of the boundary of a classical vortex patch for the 2D Euler equations were published, one by Chemin and the other by Bertozzi-Constantin. Chemin, in fact, proved a more general result, showing that vorticity initially having discontinuities only in directions normal to a family of vector fields continue to be so characterized by the time-evolved vector fields. A different, four-page 'elementary' proof of the regularity of a vortex patch boundary was published in 1994 by Ph. Serfati, employing only one vector field to describe the discontinuities in the initial data. In this talk, we discuss Serfati's proof along with a natural extension of it to a family of vector fields that reproduces the 1995 result of Chemin.