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

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March 2004, 3(1): 115-131. doi: 10.3934/cpaa.2004.3.115

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

M. Petcu ^1, , Roger Temam ^2, and D. Wirosoetisno ^3,

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, United States
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, United States

Received May 2003 Revised October 2003 Published January 2004

Abstract
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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.

Keywords: Primitive equations for the ocean, high-order regularity., energy estimates.

Mathematics Subject Classification: 35B65, 35Q40, 35J2.

Citation: M. Petcu, Roger Temam, D. Wirosoetisno. Existence and regularity results for the primitive equations in two space dimensions. Communications on Pure & Applied Analysis, 2004, 3 (1) : 115-131. doi: 10.3934/cpaa.2004.3.115

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