Construction of Steady-State Hydromagnetic Dynamos. Ii. The Spherical Conductor

摘要

The steady-state kinematic dynamo problem in a homogeneous sphere with concentric spherical fluid core is considered. The existence of a class of solenoidal dynamos satisfying a no-slip condition on the core boundary is proved by perturbing the discrete spectrum of a simpler self-adjoint comparison problem. The dynamos are of the form q = q(1) + q(2) + q(3) where q(1) is spatially periodic, q(2) is zero except in a neighborhood of the boundary of the core, and q(3) is an arbitrary sufficiently small motion. (Author)