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Kinetic formulation of vortex vector fields

Pierre Bochard and Radu Ignat

Vol. 10 (2017), No. 3, 729–756

This article focuses on gradient vector fields of unit Euclidean norm in N . The stream functions associated to such vector fields solve the eikonal equation and the prototype is given by the distance function to a closed set. We introduce a kinetic formulation that characterizes stream functions whose level sets are either spheres or hyperplanes in dimension N 3. Our main result proves that the kinetic formulation is a selection principle for the vortex vector field whose stream function is the distance function to a point.

vortex, eikonal equation, characteristics, kinetic formulation, level sets
Mathematical Subject Classification 2010
Primary: 35F21
Secondary: 35B65, 35F20
Received: 3 October 2016
Revised: 17 January 2017
Accepted: 20 February 2017
Published: 17 April 2017
Pierre Bochard
Département de Mathématiques
Université Paris-Sud 11
91405 Orsay
Radu Ignat
Institut de Mathématiques de Toulouse
Université Paul Sabatier
31062 Toulouse