Vortices, instabilities, and non-uniqueness in incompressible fluids

Abstract: Vortices form important structures in many fluids problems, such as the shear layers that form behind airplane wings. These structures also strongly influence modelling in turbulent flows. Despite their fundamental importance to fluid dynamics, vortices involve point singularities and are intimately linked with well known instabilities in fluids; for these reasons they are challenging to model and analyze mathematically. I will discuss various mathematical frameworks for describing vortices in the context of the incompressible Euler equation in two dimensions, drawing connections to both physical motivation and to outstanding questions in mathematical analysis. I will conclude by discussing recent work with Alberto Bressan, which studies how to rigorously link point vortices with non-uniqueness and unpredictability in solutions of Euler's equation.

mathematical physicsanalysis of PDEsgeneral mathematics

Audience: researchers in the topic

( paper | slides )

Comments: the meeting has ended

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Global Seminar on Mathematical Modeling and Applications

Series comments: Description: Occasional seminar on mathematical modeling and related topics

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