Existence and regularity results for the primitive equations in two space dimensions

M. Petcu; Roger Temam; D. Wirosoetisno

doi:10.3934/cpaa.2004.3.115

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2004, Volume 3, Issue 1: 115-131. Doi: 10.3934/cpaa.2004.3.115

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Existence and regularity results for the primitive equations in two space dimensions

1.
Laboratoire d'Analyse Numérique, Université de Paris-Sud, Orsay, The Institute of Mathematics of the Romanian Academy, Bucharest, Romania, The Institute for Scientific Computing and Applied Mathematics, Indiana University, Bloomington, IN
2.
The Institute for Scientific Computing and Applied Mathematics, Indiana University, 831 E. 3rd St., Rawles Hall, Bloomington, IN 47405
3.
The Institute for Scientific Computing and Applied Mathematics, Indiana University, Bloomington, IN

Received: April 30, 2003

Revised: September 30, 2003

Published: February 2004

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Abstract

Our aim in this article is to present some existence, uniqueness and regularity results for the Primitive Equations of the ocean in space dimension two with periodic boundary conditions. We prove the existence of weak solutions for the PEs, the existence and uniqueness of strong solutions and the existence of more regular solutions, up to $\mathcal C^\infty$ regularity.

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Mathematics Subject Classification: 35B65, 35Q40, 35J20.

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