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Instabilities and ill-posedness for the magnetogeostrophic equation

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Topological Dynamics in the Physical and Biological Sciences

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.

This talk is part of the Isaac Newton Institute Seminar Series series.

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