Euler equation, vortex patches and singular integrals
报告人：Joan Mateu 教授, 西班牙巴塞罗那自治大学
报告摘要：The purpose of this talk is to present the Euler equation on the plane for inviscid and incompressible fluids. Moreover, we will introduce the vorticity which is a very important quantity in fluid mechanics. We will present the vorticity equation and the vortex patches. We will explain that some vortex patches rotates and we will give a theorem of existence of rotating vortex patches. To get this result we will need to use techniques coming from harmonic analysis as singular integrals. We will use the boundedness of this singular integral operators in Holder spaces.
Joan Mateu is Professor Titular of mathematical analysis at Universitat Autònoma de Barcelona from 1995. He got the Phd in mathematics under the supervision of Professor Joan Verdera. His main topics of interest are harmonic analysis, analytic capacity and Euler equation. He has published many important papers in famous journals such as Ann of Math, J Amer Math Soc, Duke Math J, ARMA, Adv Math and Proc Lond Math Soc.