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On the nonlocal boundary value problem of geophysical fluid flows

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Abstract

This paper proposes a nonlocal formulation regarding the modeling of Antarctic Circumpolar Current by introducing flow functions to encode horizontal flow components without considering vertical motion. Using topological degree, zero exponent theory and fixed point technique, we show the existence of positive solutions to nonlocal boundary value problems with nonlinear vorticity.

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Acknowledgements

The authors are grateful to the referees for their careful reading of the manuscript and their valuable comments. We thank the editor also. There are no conflicts of interest to this work.

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Authors and Affiliations

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

    JinRong Wang & Wenlin Zhang

  2. 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

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

    Michal Fečkan

  4. School of Mathematical Sciences, Qufu Normal University, Qufu, 273165, Shandong, China

    JinRong Wang

  5. School of Mathematics and Computer Science, Liupanshui Normal University, Liupanshui, 553004, Guizhou, China

    Wenlin Zhang

Authors
  1. JinRong Wang
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  2. Michal Fečkan
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  3. Wenlin Zhang
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Correspondence to JinRong Wang, Michal Fečkan or Wenlin Zhang.

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This work is partially supported by the National Natural Science Foundation of China (11661016), Training Object of High Level and Innovative Talents of Guizhou Province ((2016)4006), Major Research Project of Innovative Group in Guizhou Education Department ([2018]012), Guizhou Data Driven Modeling Learning and Optimization Innovation Team ([2020]5016), the Slovak Research and Development Agency under the contract No. APVV-18-0308, and the Slovak Grant Agency VEGA No. 1/0358/20 and No. 2/0127/20.

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Wang, J., Fečkan, M. & Zhang, W. On the nonlocal boundary value problem of geophysical fluid flows. Z. Angew. Math. Phys. 72, 27 (2021). https://doi.org/10.1007/s00033-020-01452-z

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  • DOI: https://doi.org/10.1007/s00033-020-01452-z

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