Active Scalar Equations and a Geodynamo Model. Speaker: Susan Friedlander

Location: Old Geology, Theatre 1
We discuss an advection-diffusion equation that has been
proposed by Keith Moffatt as a model for the Geodynamo. Even
though the drift velocity can be strongly singular, we prove
that the critically diffusive PDE is globally well-posed.
We examine the nonlinear instability of a particular steady
state and use continued fractions to construct a lower bound
on the growth rate of a solution. This lower bound grows as
the inverse of the diffusivity coefficient. In the Earth's
fluid core this coefficient is expected to be very small.
Thus the model does indeed produce very strong Geodynamo action.

This work is joint with Vlad Vicol.