# American Institute of Mathematical Sciences

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August  2019, 39(8): 4771-4781. doi: 10.3934/dcds.2019194

## Study of a nonlinear boundary-value problem of geophysical relevance

 Faculty of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, 1090 Wien, Austria

* Corresponding author: Kateryna Marynets

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

Received  October 2018 Revised  December 2018 Published  May 2019

Fund Project: The author is supported by the WWTF research grant MA16-009.

We present some results on the existence and uniqueness of solutions of a two-point nonlinear boundary value problem that arises in the modeling of the flow of the Antarctic Circumpolar Current.

Citation: Kateryna Marynets. Study of a nonlinear boundary-value problem of geophysical relevance. Discrete & Continuous Dynamical Systems - A, 2019, 39 (8) : 4771-4781. doi: 10.3934/dcds.2019194
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##### References:
Depiction of the azimuthal and polar spherical coordinates $\varphi \in [0,2\pi)$ and $\theta \in [0,\pi]$ of a point $P$ on the spherical surface of the Earth: $\theta = 0$ corresponds to the North Pole and $\theta = \pi/2$ to the Equator
The unit vectors of the coordinate system on the eastward rotating spherical Earth, with $e_{\varphi}$ pointing in the azimuthal direction
Depiction of the stereographic projection $P \mapsto P'$ from the North Pole to the equatorial plane, illustrated for a location that corresponds to the region where the Antarctic Circumplolar Current is encountered
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