| Abstract: |
| We consider the stability and long time behavior of the inviscid magnetohydrodynamics equations with magnetic dissipation near a combination of a shear flow and a constant magnetic field. While the linearized equations around this stationary solution are stable in Sobolev regularity, we show that in any small analytic neighborhood there exist non-trivial low frequency solutions of the nonlinear problem, which are unstable.
More precisely, we show that the critical regularity of the corresponding linearized problem is given by a
Gevrey class. This talk is based on joint work with Niklas Knobel. |
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