Instabilities and ill-posedness for the magnetogeostrophic equation
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| Description: |
Friedlander, S (University of Southern California)
Tuesday 24 July 2012, 14:00-14:40 |
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| Created: | 2012-07-31 10:16 |
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| Collection: | Topological Dynamics in the Physical and Biological Sciences |
| Publisher: | Isaac Newton Institute |
| Copyright: | Friedlander, S |
| Language: | eng (English) |
| 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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