The question of whether it is possible to have a kinematic magnetic dynamo for a conducting fluid with time-independent (steady) velocity field v(x) and vanishingly small electrical resistivity has remained an open question in the understanding of the origin of magnetic fields in nature. By considering the zero resistivity dynamics, examples of steady dynamos are found. Analysis of these examples supports the conjecture that, for sufficiently small resistivity, 2 dynamo action can occur in typical, smooth, steady, three-dimensional, chaotic fluid flows.
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Finn et al. (1989) studied this question.
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