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Existence and stability results for a second-order differential equation for the Antarctic circumpolar current

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Abstract

In this paper, we derive a new integral equation model for the Antarctic circumpolar current (ACC) by considering the radial solutions for a semi-linear elliptic equation model of gyres and applying Green’s function. We give the representation of solutions for constant vorticity and linear vorticity and show the existence and uniqueness of solutions for nonlinear vorticity. Finally, we present the Ulam–Hyers stability for the ACC involving Lipschitz-type nonlinear vorticity.

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Acknowledgements

The authors are grateful to the referees for their careful reading of the manuscript and valuable comments. The authors thank the help from the editor too.

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Authors and Affiliations

  1. Department of Mathematics, Guizhou University, Guiyang, 550025, Guizhou, China

    Fei Chen & JinRong Wang

  2. Supercomputing Algorithm and Application Laboratory of Guizhou University and Gui’an Scientific Innovation Company, Guizhou University, Guiyang, 550025, Guizhou, China

    Fei Chen & JinRong Wang

  3. Department of Mathematical Analysis and Numerical Mathematics, Faculty of Mathematics, Physics and Informatics, Comenius University in Bratislava, Mlynská dolina, 842 48, Bratislava, Slovakia

    Michal Fečkan

  4. Mathematical Institute, Slovak Academy of Sciences, Štefánikova 49, 814 73, Bratislava, Slovakia

    Michal Fečkan

Authors
  1. Fei Chen
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  2. Michal Fečkan
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  3. JinRong Wang
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Correspondence to JinRong Wang.

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Communicated by Adrian Constantin.

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This work is partially supported by the National Natural Science Foundation of China (12161015), Guizhou Provincial Basic Research Program (Natural Science) [2023]034, the Slovak Research and Development Agency under the Contract No. APVV-18-0308, and the Slovak Grant Agency VEGA Nos. 2/0127/20 and 1/0084/23.

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Chen, F., Fečkan, M. & Wang, J. Existence and stability results for a second-order differential equation for the Antarctic circumpolar current. Monatsh Math 203, 809–824 (2024). https://doi.org/10.1007/s00605-023-01868-5

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  • DOI: https://doi.org/10.1007/s00605-023-01868-5

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