Preprint
A free boundary approach to the Rosensweig instability of ferrofluids
Abstract
We establish the existence of saddle points for a free boundary problem describing the two-dimensional free surface of a ferrofluid which undergoes normal field instability (also known as Rosensweig instability). The starting point consists in the ferro-hydrostatic equations for the magnetic potentials in the ferrofluid and air, and the function describing their interface. The former constitute the strong form for the Euler-Lagrange equations of a convex-concave functional. We extend this functional in order to include interfaces that are not necessarily graphs of functions. Saddle points are then found by iterating the direct method of the calculus of variations and by applying classical results of convex analysis. For the existence part we assume a general (arbitrary) non linear magnetization law. We also treat the case of a linear law: we show, via convex duality arguments, that the saddle point is a constrained minimizer of the relevant energy functional of the physical problem.
Citation
arXiv:1704.05722 [math.AP]Citation
@article{urn:nbn:de:hebis:34-2017042452416,
author={Parini, Enea and Stylianou, Athanasios},
title={A free boundary approach to the Rosensweig instability of ferrofluids},
year={2017}
}
0500 Oax 0501 Text $btxt$2rdacontent 0502 Computermedien $bc$2rdacarrier 1100 2017$n2017 1500 1/eng 2050 ##0##urn:nbn:de:hebis:34-2017042452416 3000 Parini, Enea 3010 Stylianou, Athanasios 4000 A free boundary approach to the Rosensweig instability of ferrofluids / Parini, Enea 4030 4060 Online-Ressource 4085 ##0##=u http://nbn-resolving.de/urn:nbn:de:hebis:34-2017042452416=x R 4204 \$dPreprint 4170 Mathematische Schriften Kassel ;; 17, 01 7136 ##0##urn:nbn:de:hebis:34-2017042452416
2017-04-24T13:01:11Z 2017-04-24T13:01:11Z 2017-04-18 urn:nbn:de:hebis:34-2017042452416 http://hdl.handle.net/123456789/2017042452416 eng Urheberrechtlich geschützt https://rightsstatements.org/page/InC/1.0/ ferrofluids free boundary problem convex-concave functional 510 A free boundary approach to the Rosensweig instability of ferrofluids Preprint We establish the existence of saddle points for a free boundary problem describing the two-dimensional free surface of a ferrofluid which undergoes normal field instability (also known as Rosensweig instability). The starting point consists in the ferro-hydrostatic equations for the magnetic potentials in the ferrofluid and air, and the function describing their interface. The former constitute the strong form for the Euler-Lagrange equations of a convex-concave functional. We extend this functional in order to include interfaces that are not necessarily graphs of functions. Saddle points are then found by iterating the direct method of the calculus of variations and by applying classical results of convex analysis. For the existence part we assume a general (arbitrary) non linear magnetization law. We also treat the case of a linear law: we show, via convex duality arguments, that the saddle point is a constrained minimizer of the relevant energy functional of the physical problem. open access arXiv:1704.05722 [math.AP] Parini, Enea Stylianou, Athanasios Mathematische Schriften Kassel ;; 17, 01 35R35 49J35 35Q61 35Q35 Mathematische Schriften Kassel 17, 01
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