Fast Dynamo Action On The 3-Torus For Pulsed-Diffusions

Uploaded May 2026 | Updated September 2026, 3 weeks ago

Analysis and Mathematical Physics
2:30pm|Simonyi Hall 101 and Remote Access
Topic: Fast Dynamo Action On The 3-Torus For Pulsed-Diffusions
Speaker: Massimo Sorella
Affiliation: Imperial College London
Date: May 5, 2026

For the passive vector equation, the fast dynamo conjecture predicts exponential-in-time growth of the L2 norm of the solution under the Lipschitz flow generated by a vector field, at a rate independent of the resistivity. We prove this conjecture for the pulsed diffusion model with a time-periodic stretch-fold-shear (SFS) vector field. Our approach relies on anisotropic Banach spaces adapted to the underlying flow dynamics. In the zero-diffusivity regime, we establish the existence of a distributional eigenfunction of the time-one solution operator corresponding to a discrete eigenvalue of modulus greater than one, and then treat the resistive term as a perturbation in these spaces.

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