American Institute of Mathematical Sciences

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

 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

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.
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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