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Stability properties of nontrivial periodic water waves for fixed-depth rotational equatorial flows

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Abstract

We investigate the local stability for fixed-depth rotational equatorial flows. We first obtain the precise formula of the second derivative of bifurcation parameters at the bifurcation point. In particular, their signs can be assessed when vorticity is small enough and the mean depth is small or large enough. Furthermore, we study the stability property for periodic traveling waves of the thermocline near the equator with a fixed mean depth. For this aim, we obtain a new stability exchange formula which improves the famous Crandall-Rabinowitz stability exchange theorem.

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There is not any conflict of interest. Data sharing not applicable to this article as no datasets were generated or analysed during the current study.

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Authors and Affiliations

  1. School of Mathematical Sciences, Dalian University of Technology, Dalian, 116024, People’s Republic of China

    Guowei Dai & Siyu Gao

  2. School of Mathematics and Statistics, Xidian University, Xi’an, 710071, People’s Republic of China

    Ruyun Ma

  3. School of Mathematical Sciences, Jiangsu University, Zhenjiang, 212000, People’s Republic of China

    Yong Zhang

Authors
  1. Guowei Dai
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  2. Siyu Gao
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  3. Ruyun Ma
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  4. Yong Zhang
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Contributions

GD and SG wrote the main manuscript text and RM and YZ made revisions to this article. All authors reviewed the manuscript.

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Correspondence to Guowei Dai.

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Research supported by NNSF of China (Nos. 12371110, 12301133, 12061064) and Xing Liao Yingcai Plan (No. XLYC2203045).

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Dai, G., Gao, S., Ma, R. et al. Stability properties of nontrivial periodic water waves for fixed-depth rotational equatorial flows. Anal.Math.Phys. 14, 6 (2024). https://doi.org/10.1007/s13324-023-00863-1

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  • DOI: https://doi.org/10.1007/s13324-023-00863-1

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