### Instabilities and ill-posedness for the magnetogeostrophic equation

Friedlander, S *(University of Southern California)*

Tuesday 24 July 2012, 14:00-14:40

Seminar Room 1, Newton Institute

#### Abstract

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.

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