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Asymptotics for vortex filaments using a modified Biot-Savart kernel
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Pooley, Benjamin C. and Rodrigo Diez, José L. (2020) Asymptotics for vortex filaments using a modified Biot-Savart kernel. Journal of Mathematical Analysis and Applications, 485 (1). 123755. doi:10.1016/j.jmaa.2019.123755 ISSN 0022-247X.
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Official URL: http://dx.doi.org/10.1016/j.jmaa.2019.123755
Abstract
We consider a family of approximations to the Euler equations obtained by adding to the non-locality in the Biot-Savart kernel together with a mollification (with parameter ε). We consider the evolution of a thin vortex tube. We show that the velocity on the filament (core of the tube) in the limit as is given where κ and B are the curvature and binormal of the curve, and C, are uniformly bounded.
| Item Type: | Journal Article | ||||||||
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| Subjects: | Q Science > QA Mathematics | ||||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||
| SWORD Depositor: | Library Publications Router | ||||||||
| Library of Congress Subject Headings (LCSH): | Viscous flow -- Mathematics, Vortex-motion -- Mathematical models, Lagrange equations -- Numerical solutions | ||||||||
| Journal or Publication Title: | Journal of Mathematical Analysis and Applications | ||||||||
| Publisher: | Academic Press | ||||||||
| ISSN: | 0022-247X | ||||||||
| Official Date: | 1 May 2020 | ||||||||
| Dates: |
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| Volume: | 485 | ||||||||
| Number: | 1 | ||||||||
| Article Number: | 123755 | ||||||||
| DOI: | 10.1016/j.jmaa.2019.123755 | ||||||||
| Status: | Peer Reviewed | ||||||||
| Publication Status: | Published | ||||||||
| Access rights to Published version: | Restricted or Subscription Access | ||||||||
| Date of first compliant deposit: | 20 December 2019 | ||||||||
| Date of first compliant Open Access: | 9 December 2020 | ||||||||
| RIOXX Funder/Project Grant: |
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