Electron. J. Diff. Eqns., Vol. 2000(2000), No. 35, pp. 1-11.
### On the tidal motion around the earth complicated by the circular
geometry of the ocean's shape

Ranis N. Ibragimov

**Abstract:**

We study the Cauchy-Poisson free boundary problem on the stationary motion
of a perfect incompressible fluid circulating around the Earth.
The main goal is to find the inverse conformal mapping of the unknown
free boundary in the hodograph plane onto some fixed boundary
in the physical domain. The approximate solution to the problem is
obtained as an application of this method.
We also study the behaviour of tidal waves around the Earth. It is shown
that on a positively curved bottom the problem admits two different high
order systems of shallow water equations, while the classical problem for
the flat bottom admits only one system.
Submitted January 5, 2000. Published May 16, 2000.

Math Subject Classifications: 35Q35, 76C99.

Key Words: Cauchy-Poisson free boundary problem, shallow water theory,
conformal mapping.

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Ranis N. Ibragimov
Department of Mathematics and Statistics
University of Victoria
P.O. Box 3045 STN CSC
Victoria, B.C., V8P 2A1, Canada
e-mail: ranis@nbnet.nb.ca |

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