Asymptotic linear stability of columnar vortices driven by Coriolis force
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866917351245479936 |
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| author | Miao, Shuang Ren, Siqi Zhang, Zhifei |
| author_facet | Miao, Shuang Ren, Siqi Zhang, Zhifei |
| contents | In this paper, we establish the asymptotic linear stability of a class of Coriolis-driven columnar vortices for the 3-D axisymmetric Euler equations. This result represents a critical step toward proving the nonlinear asymptotic stability of such vortices. The key and widely applicable strategy is to construct a distorted Fourier basis, which is achieved by solving a two-parameter $(c, ξ)$-dependent Schrödinger equation associated with the linearized operator of the system. To capture the precise asymptotic behavior of the solution, we decompose the $c-ξ$ plane into distinct regions, with the partitioning guided by the leading-order profiles of the Schrödinger equation across different parameter regimes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_17268 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Asymptotic linear stability of columnar vortices driven by Coriolis force Miao, Shuang Ren, Siqi Zhang, Zhifei Analysis of PDEs In this paper, we establish the asymptotic linear stability of a class of Coriolis-driven columnar vortices for the 3-D axisymmetric Euler equations. This result represents a critical step toward proving the nonlinear asymptotic stability of such vortices. The key and widely applicable strategy is to construct a distorted Fourier basis, which is achieved by solving a two-parameter $(c, ξ)$-dependent Schrödinger equation associated with the linearized operator of the system. To capture the precise asymptotic behavior of the solution, we decompose the $c-ξ$ plane into distinct regions, with the partitioning guided by the leading-order profiles of the Schrödinger equation across different parameter regimes. |
| title | Asymptotic linear stability of columnar vortices driven by Coriolis force |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2603.17268 |