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Vortex filament dynamics

[Moved Online] Introductory Workshop: Mathematical problems in fluid dynamics January 25, 2021 - February 05, 2021

January 29, 2021 (10:00 AM PST - 11:00 AM PST)
Speaker(s): Valeria Banica (Sorbonne University, Laboratoire Jacques-Louis Lions)
Location: MSRI: Online/Virtual
Tags/Keywords
  • vortex filaments

Primary Mathematics Subject Classification No Primary AMS MSC
Secondary Mathematics Subject Classification No Secondary AMS MSC
Video

Vortex Filament Dynamics

Abstract

A 3-D fluid displays a vortex filament if its vorticity is highly concentrated around a curve in space. Understanding the evolution of vortex filaments is a natural but challenging question, as this situation does not enter the framework of the general results available for 3-D incompressible Euler. It is conjectured that the binormal flow has an important role in the dynamics of one or several vortex filaments. This model was derived formally at the beginning of the last century and is at the heart of recent researches. In this lecture I will talk about the state of the art of deriving models for vortex filaments dynamics, as well as about mathematical methods and results for the binormal flow and some related models.

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Vortex Filament Dynamics

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