Instabilities and ill-posedness for the magnetogeostrophic equation
Seminar Room 1, Newton Institute
We discuss an active scalar equation that is motivated by a model presented by Keith Moffatt for the geodynamo and magnetogeostrophic turbulence in the Earth's fluid core. We prove that the non-difusive equation is Lipshitz ill-posed in Sobolev spaces. In contrast, the diffusive equation is globally well-posed. In this case we give an example of a steady state that is nonlinearly unstable, and hence produces a dynamo effect in the sense of an exponentially growing magnetic field.
This is joint work with Vlad Vicol.