3 years ago

The Biot–Savart operator of a bounded domain

Alberto Enciso, M. Ángeles García-ferrero, Daniel Peralta-salas

Publication date: November 2018

Source: Journal de Mathématiques Pures et Appliquées, Volume 119

Author(s): Alberto Enciso, M. Ángeles García-Ferrero, Daniel Peralta-Salas

Abstract

We construct the analog of the Biot–Savart integral for bounded domains. Specifically, we show that the velocity field of an incompressible fluid with tangency boundary conditions on a bounded domain can be written in terms of its vorticity using an integral kernel KΩ(x,y) that has an inverse-square singularity on the diagonal.

Résumé

On construit l'analogue de l'intégrale de Biot–Savart pour un domain borné. Plus précisément, en supposant comme condition aux limites que le champ de vitesse d'un fluide incompressible est tangent à la frontière, on montre qu'on peut écrire la vitesse en termes de la vorticité en utilisant un noyau intégral KΩ(x,y) qui diverge comme l'inverse du carré sur la diagonale.

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