Existence and uniqueness of strong periodic solutions of theprimitive equations of the ocean

T. Tachim Medjo

doi:10.3934/dcds.2010.26.1491

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2010, Volume 26, Issue 4: 1491-1508. Doi: 10.3934/dcds.2010.26.1491

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

T. Tachim Medjo^1,

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

Received: August 31, 2008

Revised: January 31, 2009

Published: November 2010

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Abstract

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.

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Mathematics Subject Classification: 35K45, 35B10, 35K55.

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