On the nonlocal boundary value problem of geophysical fluid flows

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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Correspondence to JinRong Wang or 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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Keywords

  • Nonlocal boundary value problem
  • Positive solutions
  • Fredholm operator
  • Leray–Schauder degree

Mathematics Subject Classification

  • 34A34
  • 45G15
  • 76B03