Dynamics of Partial Differential Equations

Volume 18 (2021)

Number 3

A new approach to study constant vorticity water flows in the $\beta$-plane approximation with centripetal forces

Pages: 199 – 210

DOI: https://dx.doi.org/10.4310/DPDE.2021.v18.n3.a2


Fahe Miao (Department of Mathematics, Guizhou University, Guiyang, Guizhou, China)

Michal Fečkan (Dept. of Mathematical Analysis and Numerical Mathematics, Faculty of Mathematics, Physics and Informatics, Comenius University in Bratislava, Slovakia; and Mathematical Institute, Slovak Academy of Sciences, Bratislava, Slovakia)

Jinrong Wang (School of Mathematical and Information Sciences, Guiyang University, Guiyang, Guizhou, China)


In this paper, we study three-dimensional equatorial flows with constant vorticity beneath a wave train and above a flat bed in the $\beta$-plane approximation with centripetal forces by adopting higher order approximation about the Coriolis terms. We show that the new approximation about the Coriolis forces is also applicable for certain problem, which help us to derive the same result.


constant vorticity, equatorial flows, $\beta$-plane, centripetal forces

2010 Mathematics Subject Classification

35J60, 35Q31, 76B15

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), 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.

Received 19 January 2021

Published 22 July 2021