Vortex filament dynamics

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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