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arXiv · 2602.07807

Instability of shear flows with neutral embedded eigenvalues

Hui Li·Siqi Ren·Yuxi Wang·Guoqing Zhang
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Abstract

We study the linear stability of a class of monotone shear flows. When the associated Rayleigh operator possesses a neutral embedded eigenvalue, we show that solutions of the linearized system may exhibit arbitrarily large growth in both the $L^\infty$ and $L^2$ norms. Moreover, when the embedded eigenvalue is multiple, we prove that the instability becomes stronger and explicitly construct solutions that grow linearly in time. This instability originates from the non-normality of the Rayleigh operator.

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Hui Li, Siqi Ren, Yuxi Wang, Guoqing Zhang. 2026-02-08. Instability of shear flows with neutral embedded eigenvalues. https://arxiv.org/abs/2602.07807

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