中科院数学与系统科学研究院
数学研究所
学术报告
偏微分方程研讨班
报告人： Prof. Giovanni Leoni （Carnegie Mellon University）
题 目：On Hardy-type inequalities in fractional Sobolev spaces
时 间：2022.01.13（星期四），21:00-22:00
地 点：Zoom会议：954 6614 0736 密码：71VTVy
摘 要：In this talk, we will discuss the Lions-Magenes spaces $W^{1/p,p}_00(\Omega)$ in (unbounded) Lipschitz domains and their connections with Hardy's type inequalities.
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报告人： Prof. Manuel Del Pino（University of Bath）
题 目：Dynamics of concentrated vorticities in 2d and 3d Euler flows
时 间：2022.01.20（星期四），21:00-22:00
地 点：Zoom会议：933 2635 8203 密码：SeCNS9
摘 要：A classical problem that traces back to Helmholtz and Kirchhoff is the understanding of the dynamics of solutions to the Euler equations of an inviscid incompressible fluid when the vorticity of the solution is initially concentrated near isolated points in 2d or vortex lines in 3d. We discuss some recent results on the existence and asymptotic behaviour of these solutions. We describe, with precise asymptotics, interacting vortices, and travelling helices. We rigorously establish the law of motion of ”leapfrogging vortex rings”, originally conjectured by Helmholtz in 1858.
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