A Subsequentially Fast Dynamo on \(\mathbb {T}^3\)

Abstract

We construct a smooth velocity field u on \(\mathbb {R}_+ \times \mathbb {T}^3\) that exhibits kinematic dynamo action, causing exponential growth in solutions to the magnetohydrodynamic induction equation, uniformly over a suitable sequence of diffusivities \(\kappa _j \rightarrow 0\) and times \(t^j_\ell {\mathop {\rightarrow }\limits ^{\ell \rightarrow \infty }} \infty \). We call this a subsequentially fast dynamo.