Instability of shear flows with neutral embedded eigenvalues
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866914314322968576 |
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| author | Li, Hui Ren, Siqi Wang, Yuxi Zhang, Guoqing |
| author_facet | Li, Hui Ren, Siqi Wang, Yuxi Zhang, Guoqing |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_07807 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Instability of shear flows with neutral embedded eigenvalues Li, Hui Ren, Siqi Wang, Yuxi Zhang, Guoqing Analysis of PDEs 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. |
| title | Instability of shear flows with neutral embedded eigenvalues |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2602.07807 |