On three-dimensional geophysical capillary–gravity water flows with constant vorticity

Abstract

Consideration in this paper is three-dimensional capillary–gravity water flows governed by the geophysical water wave equations with all the Coriolis terms being retained. It is proved that the merely possible flow exhibiting a constant vorticity vector captures vanishing vertical velocity, constant horizontal velocity and flat free surface.

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Acknowledgements

The work of Fan is supported by a NSFC Grant No. 11701155. The work of Gao is partially supported by the NSFC Grant No. 11531006 and Jiangsu Center for Collaborative Innovation in Geographical Information Resource Development and Application. The authors are grateful to Calin Iulian Martin for his valuable suggestions during preparation of the manuscript.

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Correspondence to Hongjun Gao.

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Fan, L., Gao, H. On three-dimensional geophysical capillary–gravity water flows with constant vorticity. Annali di Matematica (2020). https://doi.org/10.1007/s10231-020-01010-4

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Keywords

  • Capillary–gravity waves
  • Coriolis force
  • Waves in rotating fluids
  • Vorticity

Mathematics Subject Classification

  • 35Q35
  • 76B45
  • 76U05