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Approximately axisymmetric antidynamo theorems

Title data

Kaiser, Ralf:
Approximately axisymmetric antidynamo theorems.
In: SIAM Journal on Applied Mathematics. Vol. 78 (2018) Issue 6 . - pp. 3188-3212.
ISSN 1095-712X
DOI: https://doi.org/10.1137/18M1173174


Abstract in another language

The axisymmetric antidynamo theorem rules out dynamo action by the motion of a conducting fluid in a bounded domain surrounded by vacuum, provided that magnetic field, flow field, magnetic diffusivity distribution, and the shape of the domain are axisymmetric. We present in this paper three versions of a generalized axisymmetric antidynamo theorem, which establishes decay of the magnetic field even in the presence of small amounts of nonaxisymmetry in the magnetic field, the flow field, and the diffusivity distribution. The first two versions hold only in the case of weak variations of compressibility and diffusivity of the fluid, whereas the third version is not subject to such a restriction. By proper choice of the diffusivity distribution modeling the conducting domain the third version allows even small deviations from axisymmetry of this domain. However the smallness requirements of the third version are not as explicit as in the other versions and they are generally more severe. The first version refers only to the meridional part of the axisymmetric magnetic field and proves monotonic decay to zero of the corresponding scalar in the energy norm, whereas the other two versions demonstrate decay of functionals that involve both the meridional as well as the azimuthal scalars and the magnetic field itself. The smallness of the nonaxisymmetric part of the magnetic field is controlled by the ratio of energies of the nonaxisymmetric over the axisymmetric part, whereas the nonaxisymmetric parts of flow field and diffusivity distribution are controlled by their maximum values.

Further data

Item Type: Article in a journal
Refereed: Yes
Subject classification: Mathematics Subject Classification Code: 76W05 (85A30 86A25)
Institutions of the University: Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics VI (Nonlinear Analysis and Mathematical Physics) > Chair Mathematics VI (Nonlinear Analysis and Mathematical Physics) - Univ.-Prof. Dr. Thomas Kriecherbauer
Result of work at the UBT: Yes
DDC Subjects: 500 Science > 510 Mathematics
Date Deposited: 22 Mar 2021 09:40
Last Modified: 22 Mar 2021 09:40
URI: https://eref.uni-bayreuth.de/id/eprint/64145