Analysis and Mathematical Physics

For the passive vector equation, the fast dynamo conjecture predicts exponential-in-time growth of the $L^2$ 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.