Kinetic formulation of vortex vector fields
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 stre...
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| creator | Bochard, Pierre Ignat, Radu |
| description | 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. |
| doi_str_mv | 10.48550/arxiv.1602.02961 |
| format | Article |
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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.</abstract><cop>Ithaca</cop><pub>Cornell University Library, arXiv.org</pub><doi>10.48550/arxiv.1602.02961</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Eikonal equation Fields (mathematics) Hyperplanes Mathematics - Analysis of PDEs |
| title | Kinetic formulation of vortex vector fields |
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