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arXiv · 1602.02961

Kinetic formulation of vortex vector fields

Pierre Bochard·Radu Ignat
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Abstract

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

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Pierre Bochard, Radu Ignat. 2016-02-09. Kinetic formulation of vortex vector fields. https://doi.org/10.2140/apde.2017.10.729

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