8 papers
Smooth autonomous fast dynamo action on the three-torus
Michele Coti Zelati, Massimo Sorella, David Villringer
We construct a nonempty -open family of smooth, autonomous, divergence-free velocity fields on that generate fast dynamos. The proof proceeds by first establish…
A fast dynamo on the three-torus
Michele Coti Zelati, Massimo Sorella, David Villringer
We study the kinematic dynamo equation on the three-torus and provide a rigorous proof of fast dynamo action for a time-periodic, divergence-free, Lipschitz velocity field. Our con…
A limsup fast dynamo on
Massimo Sorella, David Villringer
We construct a time-dependent, incompressible, and uniformly-in-time Lipschitz continuous velocity field on that produces exponential growth of the magnetic energy a…
Nonlinear instability for the 3D MHD equations around the Taylor-Couette flow
Víctor Navarro-Fernández, David Villringer
We study the 3D magnetohydrodynamics (MHD) equations in an annular cylinder, perturbed around the explicit steady state given by the 3D Taylor-Couette velocity field and zero magne…
Spectral instability in the smooth Ponomarenko dynamo
Víctor Navarro-Fernández, David Villringer
We consider the kinematic dynamo equations for a passive vector in describing the evolution of a magnetic f…
A Stochastic RAGE Theorem and Enhanced Dissipation for Transport Noise
Michele Coti Zelati, Martin Hairer, David Villringer
We prove a stochastic version of the classical RAGE theorem that applies to the two-point motion generated by noisy transport equations. As a consequence, we identify a necessary a…
Alpha-unstable flows and the fast dynamo problem
Michele Coti Zelati, Massimo Sorella, David Villringer
We construct a time-independent, incompressible, and Lipschitz-continuous velocity field in that generates a fast kinematic dynamo - an instability characterized by…
Enhanced Dissipation via the Malliavin Calculus
David Villringer
In this work we investigate the phenomenon of enhanced dissipation using techniques from the Malliavin Calculus. In particular, we construct a concise, elementary argument, that al…