#### Vol. 10, No. 3, 2017

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Kinetic formulation of vortex vector fields

### Pierre Bochard and Radu Ignat

Vol. 10 (2017), No. 3, 729–756
##### Abstract

This article focuses on gradient vector fields of unit Euclidean norm in ${ℝ}^{N}$. 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 $N\ge 3$. 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.

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