The regularity of the boundary of a vortex patch and commutators of singular integrals

Abstract: I will introduce briefly the vorticity form of the Euler equation in the plane and show how singular integrals appear immediately. Then I will introduce vortex patches and the problem of regularity of the boundary. I will describe some elements of a short proof I have found recently, which also solves the regularity problem for other transport equations. Commutators of singular integrals play a key role, as it is well-known.

mathematical physicsanalysis of PDEsclassical analysis and ODEs

Audience: researchers in the topic

Online Seminar "Geometric Analysis"

Series comments: We discuss recent trends related to geometric analysis in a broad sense. The general idea is to solve geometric problems by means of advanced tools in analysis. We will include a wide range of topics such as geometric flows, curvature functionals, discrete differential geometry, and numerical simulation.

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