On the spectrum of the magnetohydrodynamic mean-field alpha^2-dynamo operator
Mathematical Physics
2014-11-20 v1 Earth and Planetary Astrophysics
math.MP
Spectral Theory
Geophysics
Abstract
The existence of magnetohydrodynamic mean-field alpha^2-dynamos with spherically symmetric, isotropic helical turbulence function alpha is related to a non-self-adjoint spectral problem for a coupled system of two singular second order ordinary differential equations. We establish global estimates for the eigenvalues of this system in terms of the turbulence function alpha and its derivative alpha'. They allow us to formulate an anti-dynamo theorem and a non-oscillation theorem. The conditions of these theorems, which again involve alpha and alpha', must be violated in order to reach supercritical or oscillatory regimes.
Keywords
Cite
@article{arxiv.1004.0231,
title = {On the spectrum of the magnetohydrodynamic mean-field alpha^2-dynamo operator},
author = {Uwe Guenther and Heinz Langer and Christiane Tretter},
journal= {arXiv preprint arXiv:1004.0231},
year = {2014}
}
Comments
35 pages, 4 figures, to be published in SIAM J. Math. Anal.