GDMSeminar: Abstracts of the Talks (2021/17)

Clodoaldo Grotta Ragazzo (Sao Paulo)
Hydrodynamic Vortex on a Compact Surface: the “Steady Vortex Metric” and possible generalizations to higher dimensions

Tuesday, September 28, 2021, 15:00 GMT

Abstract: A single hydrodynamic vortex  in the unit disc moves unless it is at the centre of the disc. The motion happens due to the  interaction of the vortex and the boundary. If the Euclidean metric is replaced by the Poincaré metric, then the interaction of the vortex with the metric cancels out that with the boundary and the vortex does not move regardless of its position. A Riemannian metric on a manifold is called a "steady vortex metric" (SVM) when a single vortex in the manifold does not move regardless of its position. The Poincaré metric on the unit disk is an example of a steady vortex metric. In this seminar we will discuss the question of existence and uniqueness of SVM's in surfaces and possible generalizations to higher dimensions.