第89回金沢解析セミナー（2021/12/21）

日時：12月21日(火) 16:45–18:15 第89回金沢解析セミナー

講演者： 清水 雄貴（SHIMIZU, Yuuki）氏（東京大学大学院 数理科学研究科）

タイトル ： A current-valued solution of the Euler equation and its application

アブストラクト：Besides the Euler flow, there is another mathematical model that describes 2D incompressible and inviscid fluid flows, called the point vortex dynamics. The point vortex dynamics is formally derived from the Euler equation by assuming that the initial vorticity is a linear combination of delta functions. It is utilized as a simple model for a fluid phenomenon with a localized vortex structure. On the other hand, since the point vortex dynamics is formally derived from an Euler flow, it is far from clear whether the insights gained from using point vortex dynamics are applicable to the Euler flows as well. Therefore, in order to solve this problem, we need to establish that the point vortex dynamics is an Euler flow in a mathematically appropriate sense. In this talk, after introducing in what sense the point vortex dynamics has been justified as an Euler flow, I will show that the point vortex dynamics is justified as a weak solution of the Euler equation in the sense of de Rham currents.

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