# American Institute of Mathematical Sciences

August  2019, 39(8): 4415-4427. doi: 10.3934/dcds.2019179

## Study of an elliptic partial differential equation modelling the Antarctic Circumpolar Current

 Fakultät für Mathematik, Universität Wien, Oskar-Morgenstern-Platz 1, Wien 1090, Austria

Received  July 2018 Revised  September 2018 Published  May 2019

We consider the ocean flow of the Antarctic Circumpolar Current. Using a recently-derived model for gyres in rotating spherical coordinates, and mapping the problem on the sphere onto the plane using the Mercator projection, we obtain a boundary-value problem for a semi-linear elliptic partial differential equation. For constant and linear oceanic vorticities, we investigate existence, regularity and uniqueness of solutions to this elliptic problem. We also provide some explicit solutions. Moreover, we examine the physical relevance of these results.

Citation: Susanna V. Haziot. Study of an elliptic partial differential equation modelling the Antarctic Circumpolar Current. Discrete & Continuous Dynamical Systems - A, 2019, 39 (8) : 4415-4427. doi: 10.3934/dcds.2019179
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##### References:
The Mercator Projection for the ACC: We project the polar angle onto the $x$-axis and the azimuthal angle onto the $y$-axis. The South Pole is situated at $x = -\infty$
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