From linear to nonlinear instabilities with application to plasma columns

Dongfen Bian

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arXiv · 2606.15824

From linear to nonlinear instabilities with application to plasma columns

Dongfen Bian

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Abstract

This article addresses the problem of proving the nonlinear instability of an equilibrium starting from its linear instability when there is no existence theory for the corresponding equations. We design a general method based on the use of analytic functions to overcome this difficulty and apply it to the classical problem of the stability of a plasma column in magneto-hydrodynamics (MHD) as an illustration.

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Dongfen Bian. 2026-06-14. From linear to nonlinear instabilities with application to plasma columns. https://arxiv.org/abs/2606.15824

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