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Instabilities and ill-posedness for the magnetogeostrophic equation

Date: 
Tuesday 24th July 2012 - 14:00 to 14:40
Venue: 
INI Seminar Room 1
Session Chair: 
Eckart Meiburg
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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Presentation Material: 
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons