A subsequentially fast dynamo on ${\mathbb{T}}^3$

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, with a rate that is uniform in diffusivity, for suitable sequences of diffusivity ${\kappa }_j\to 0.$ We call this a subsequentially fast dynamo, giving dynamo behavior intermediate between a truly slow dynamo and a truly fast dynamo.