Vol. 10, No. 3, 2017

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ISSN: 1948-206X (e-only)
ISSN: 2157-5045 (print)
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 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.

Keywords
vortex, eikonal equation, characteristics, kinetic formulation, level sets
Mathematical Subject Classification 2010
Primary: 35F21
Secondary: 35B65, 35F20
Milestones
Received: 3 October 2016
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