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arXiv · 1105.1403

On the ill/well-posedness and nonlinear instability of the magneto-geostrophic equations

Susan Friedlander·Vlad C. Vicol
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Abstract

We consider an active scalar equation that is motivated by a model for magneto-geostrophic dynamics and the geodynamo. We prove that the non-diffusive equation is ill-posed in the sense of Hadamard in Sobolev spaces. In contrast, the critically diffusive equation is 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.

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Susan Friedlander, Vlad C. Vicol. 2011-05-13. On the ill/well-posedness and nonlinear instability of the magneto-geostrophic equations. https://doi.org/10.1088/0951-7715%2F24%2F11%2F001

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