Seminario EDPs y Mecánica de Fluidos

Isoperimetric problems in ideal magnetohydrodynamics

Ponente:  Wadim Gerner (Aachen University)
Fecha:  martes 12 de enero de 2021 - 11:00

In this talk I will present 3 isoperimetric problems related to ideal magnetohydrodynamics and establish their equivalence. A first variation formula, in the spirit of [1], [2] (where the Euclidean setting is considered), will be presented for arbitrary geometries of the ambient space and it will be shown that an optimal domain, if it exists at all, can never be a ball. Lastly, I will introduce a second variation inequality, which was neither considered in [1] nor [2], and show how it can be used in order to derive more information about associated energy minimisers on optimal domains. The results presented here are part of the speakers dissertation [3].