Nonlinear asymptotic stability of 2D Taylor-Couette flow in the exterior disk
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866916662824927232 |
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| author | Li, Te Zhang, Ping Zhang, Yibin |
| author_facet | Li, Te Zhang, Ping Zhang, Yibin |
| contents | In this paper, we consider the asymptotic stability of the 2D Taylor-Couette flow in the exterior disk, with a small kinematic viscosity $ν\ll 1$ and a large rotation coefficient $|B|$. Due to the degeneracy of the Taylor-Couette flow at infinity, we cannot expect the solution to decay exponentially in a space-time decoupled manner. As stated in previous work \cite{LZZ-25}, even space-time coupled exponential decay can not be expected, and at most, we can obtain space-time coupled polynomial decay. To handle the space-time coupled decay multiplier, the previous time-independent resolvent estimate methods no longer work. Therefore, this paper introduces time-dependent resolvent estimates to deal with the space-time coupled decay multiplier $Λ_k$. We remark that the choice of $Λ_k$ is not unique, here we just provide one way to construct it. Finally, as an application, we derive a transition threshold bound of $\frac12$, which is the same as that for the Taylor-Couette flow in the bounded region. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_20253 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Nonlinear asymptotic stability of 2D Taylor-Couette flow in the exterior disk Li, Te Zhang, Ping Zhang, Yibin Analysis of PDEs In this paper, we consider the asymptotic stability of the 2D Taylor-Couette flow in the exterior disk, with a small kinematic viscosity $ν\ll 1$ and a large rotation coefficient $|B|$. Due to the degeneracy of the Taylor-Couette flow at infinity, we cannot expect the solution to decay exponentially in a space-time decoupled manner. As stated in previous work \cite{LZZ-25}, even space-time coupled exponential decay can not be expected, and at most, we can obtain space-time coupled polynomial decay. To handle the space-time coupled decay multiplier, the previous time-independent resolvent estimate methods no longer work. Therefore, this paper introduces time-dependent resolvent estimates to deal with the space-time coupled decay multiplier $Λ_k$. We remark that the choice of $Λ_k$ is not unique, here we just provide one way to construct it. Finally, as an application, we derive a transition threshold bound of $\frac12$, which is the same as that for the Taylor-Couette flow in the bounded region. |
| title | Nonlinear asymptotic stability of 2D Taylor-Couette flow in the exterior disk |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2503.20253 |