Abstract for the talk on 06.04.2016 (14:00 h)Arbeitsgemeinschaft ANGEWANDTE ANALYSIS
Pierre Bochard (Université Paris-Sud)
A kinetic characterization of vortices
Motivated by the study of a micromagnetic enery, Jabin, Otto and Perthame proved in a 2002’s paper that in dimension 2, we can select curl-free unit-lenght vector field through a kinetic formulation. Roughly speaking, this kinetic formulation excludes curl-free unit-lenght vector field which are singular along ℋ1-set to keep only solutions with point-like singularities. We will give a natural generalization to this kinetic formulation in any dimension and show that if the dimension is strictly greater than 2, it becomes much more rigid as it characterizes constant vector field or vortices, that is ±; if we have enough time, we will show how this is related with totally umbilical surfaces.