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.

DOI: S0021782417301800

You might also like
Discover & Discuss Important Research

Keeping up-to-date with research can feel impossible, with papers being published faster than you'll ever be able to read them. That's where Researcher comes in: we're simplifying discovery and making important discussions happen. With over 19,000 sources, including peer-reviewed journals, preprints, blogs, universities, podcasts and Live events across 10 research areas, you'll never miss what's important to you. It's like social media, but better. Oh, and we should mention - it's free.

Researcher displays publicly available abstracts and doesn’t host any full article content. If the content is open access, we will direct clicks from the abstracts to the publisher website and display the PDF copy on our platform. Clicks to view the full text will be directed to the publisher website, where only users with subscriptions or access through their institution are able to view the full article.