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Local and Global Analysis for Discontinuous Atmospheric Ekman Equations

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Abstract

In this paper, we extend the classical atmospheric Ekman equations to discontinuous differential equations of Ekman flows by considering the eddy viscosity with piecewise form. Local and global analysis for the corresponding discontinuous ODEs are studied respectively. In the section of local analysis, all the possible crossings of solutions are presented over the certain discontinuity linear subspaces associated with a curve. In the section of global analysis, crossings of solutions, bounded and unbounded solutions on dynamics are obtained.

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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.

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Authors and Affiliations

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

    JinRong Wang & Yi Guan

  2. Department of Mathematical Analysis and Numerical Mathematics, Faculty of Mathematics, Physics and Informatics, Comenius University in Bratislava, 842 48, Mlynská dolina, 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. Department of Mathematics and Information Science, Guiyang University, Guiyang, 550005, Guizhou, China

    Yi Guan

Authors
  1. JinRong Wang
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  2. Michal Fečkan
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  3. Yi Guan
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Correspondence to Michal Fečkan.

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This work is partially supported by the National Natural Science Foundation of China (11661016), the Training Object of High Level and Innovative Talents of Guizhou Province ((2016)4006), the 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. & Guan, Y. Local and Global Analysis for Discontinuous Atmospheric Ekman Equations. J Dyn Diff Equat 35, 663–677 (2023). https://doi.org/10.1007/s10884-021-10037-x

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  • DOI: https://doi.org/10.1007/s10884-021-10037-x

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