# American Institute of Mathematical Sciences

August  2019, 39(8): 4713-4729. doi: 10.3934/dcds.2019191

## Steady periodic equatorial water waves with vorticity

 1 Department of Mathematics, Shanghai Normal University, Shanghai 200234, China 2 Institute for Applied Mathematics, Leibniz Universität Hannover, Hannover 30167, Germany

* Corresponding author: Jifeng Chu

The paper is for the special theme: Mathematical Aspects of Physical Oceanography, organized by Adrian Constantin.

Received  September 2018 Revised  January 2019 Published  May 2019

Fund Project: Jifeng Chu was supported by the Alexander von Humboldt-Stiftung of Germany, and the National Natural Science Foundation of China (Grants No. 11671118 and No. 11871273).

Of concern are steady two-dimensional periodic geophysical water waves of small amplitude near the equator. The analysis presented here is based on the bifurcation theory due to Crandall-Rabinowitz. Dispersion relations for various choices of the vorticity distribution, including constant, affine, and some nonlinear vorticities are obtained.

Citation: Jifeng Chu, Joachim Escher. Steady periodic equatorial water waves with vorticity. Discrete & Continuous Dynamical Systems - A, 2019, 39 (8) : 4713-4729. doi: 10.3934/dcds.2019191
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