# American Institute of Mathematical Sciences

October  2010, 26(4): 1491-1508. doi: 10.3934/dcds.2010.26.1491

## Existence and uniqueness of strong periodic solutions of the primitive equations of the ocean

 1 Department of Mathematics, Florida International University, DM413B, University Park, Miami, Florida 33199, United States

Received  September 2008 Revised  February 2009 Published  December 2009

In this article, we study the existence and uniqueness of the global and periodic strong solutions of the primitive equations of the ocean. We prove that there exists a unique periodic strong solution provided that the heat source is regular and small enough. The proof of the existence is based on approximate solutions and a fixed point argument. We also derive some a priori estimates on the strong solutions.
Citation: T. Tachim Medjo. Existence and uniqueness of strong periodic solutions of the primitive equations of the ocean. Discrete & Continuous Dynamical Systems - A, 2010, 26 (4) : 1491-1508. doi: 10.3934/dcds.2010.26.1491
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