Constructs divergence-free velocity fields and magnetic fields solving the kinematic dynamo equation on arbitrary smooth bounded domains in R^3 with arbitrarily fast magnetic energy growth uniformly as diffusivity vanishes, using convex integration with explicit potentials, and unifies the approach,
Rowan,A subsequentially fast dynamo onT 3, arXiv e-prints (May 2025), arXiv:2505.23936, available at 2505.23936
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Rigorous proof of fast dynamo action on the three-torus for a time-periodic Lipschitz divergence-free velocity field, using stretch-fold-shear hyperbolic flow and anisotropic Banach spaces to obtain a spectral gap that persists under vanishing resistivity.
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Turbulent Dynamos on Bounded Domains and Their Generalization to the Geometric Transport Equation
Constructs divergence-free velocity fields and magnetic fields solving the kinematic dynamo equation on arbitrary smooth bounded domains in R^3 with arbitrarily fast magnetic energy growth uniformly as diffusivity vanishes, using convex integration with explicit potentials, and unifies the approach,
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A fast dynamo on the three-torus
Rigorous proof of fast dynamo action on the three-torus for a time-periodic Lipschitz divergence-free velocity field, using stretch-fold-shear hyperbolic flow and anisotropic Banach spaces to obtain a spectral gap that persists under vanishing resistivity.