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arXiv · 1702.04327

The Biot-Savart operator of a bounded domain

Alberto Enciso·Maria de los Angeles Garcia-Ferrero·Daniel Peralta-Salas
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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 $K_\Omega(x,y)$ that has an inverse-square singularity on the diagonal.

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Alberto Enciso, Maria de los Angeles Garcia-Ferrero, Daniel Peralta-Salas. 2017-02-14. The Biot-Savart operator of a bounded domain. https://arxiv.org/abs/1702.04327

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