# On the Spectrum of the Magnetohydrodynamic Mean-Field α2-Dynamo Operator

@article{Gnther2010OnTS,
title={On the Spectrum of the Magnetohydrodynamic Mean-Field $\alpha$2-Dynamo Operator},
author={Uwe G{\"u}nther and Heinz Langer and Christiane Tretter},
journal={SIAM J. Math. Anal.},
year={2010},
volume={42},
pages={1413-1447}
}
• Published 1 April 2010
• Mathematics, Physics
• SIAM J. Math. Anal.
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…
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