Instabilities and illposedness for the magnetogeostrophic equation
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If you have a question about this talk, please contact Mustapha Amrani.
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 nondifusive equation is Lipshitz illposed in Sobolev spaces. In contrast, the diffusive equation is globally wellposed. 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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