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

Pages: 115 - 131, Volume 3, Issue 1, March 2004

doi:10.3934/cpaa.2004.3.115       Abstract        Full Text (241.1K)       Related Articles

M. Petcu - 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 (email)
Roger Temam - The Institute for Scientific Computing and Applied Mathematics, Indiana University, 831 E. 3rd St., Rawles Hall, Bloomington, IN 47405, United States (email)
D. Wirosoetisno - The Institute for Scientific Computing and Applied Mathematics, Indiana University, Bloomington, IN, United States (email)

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.

Keywords:  Primitive equations for the ocean, energy estimates, high-order regularity.
Mathematics Subject Classification:  35B65, 35Q40, 35J20.

Received: May 2003;      Revised: October 2003;      Published: January 2004.