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Some nonlinear stability results for a magnetic induction equation with Hall, ion-slip and shear effects: necessary and sufficient condition

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Abstract

We study the nonlinear stability, with respect to axisymmetric perturbations, of the solution magnetic field to the induction equation for a weakly ionized gas, subjected to an assigned planar velocity field which, in a special case, keeps it in proximity of a gravitational center. In other cases, this velocity field can generate hyperbolic trajectories. Whatever, assuming the presence of Hall and ion-slip effects, we will try to determine how the geometric and kinematic characteristics of the gas stream affect the stability/instability of the magnetic field. Then, we obtain a necessary and sufficient stability condition and estimate the radius of attraction.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, University of Catania, Catania, Italy

    S. Lombardo

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  1. S. Lombardo
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Correspondence to S. Lombardo.

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Lombardo, S. Some nonlinear stability results for a magnetic induction equation with Hall, ion-slip and shear effects: necessary and sufficient condition. Acta Mech 226, 1487–1495 (2015). https://doi.org/10.1007/s00707-014-1265-3

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  • DOI: https://doi.org/10.1007/s00707-014-1265-3

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