关于磁流体平均场α ^2-发电机算符的谱
On the spectrum of the magnetohydrodynamic mean-field alpha^2-dynamo operator
摘要：
具有球对称各向同性螺旋湍流函数α的磁流体动力学平均场α ^2发电机的存在性与两个奇异二阶常微分方程耦合系统的非自伴谱问题有关。我们用湍流函数α及其导数α '建立了该系统本征值的整体估计。它们使我们能够用公式表示反发电机定理和非振荡定理。这些定理的条件，其中再次涉及α和α '，必须违反，以达到超临界或振荡制度。
英文摘要：
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.
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