Large norm inflation of the current in the viscous, non-resistive magnetohydrodynamics equations

Michele Dolce; Niklas Knobel; Christian Zillinger

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arXiv · 2410.22804

Large norm inflation of the current in the viscous, non-resistive magnetohydrodynamics equations

Michele Dolce·Niklas Knobel·Christian Zillinger

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Abstract

We consider the ideally conducting, viscous magnetohydrodynamics (MHD) equations in two dimensions. Specifically, we study the nonlinear dynamics near a combination of Couette flow and a constant magnetic field in a periodic infinite channel. In contrast to the Navier-Stokes equations this system is shown to exhibit algebraic instability and large norm inflation of the magnetic current on non-perturbative time scales.

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Michele Dolce, Niklas Knobel, Christian Zillinger. 2024-10-30. Large norm inflation of the current in the viscous, non-resistive magnetohydrodynamics equations. https://arxiv.org/abs/2410.22804

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