# American Institute of Mathematical Sciences

April  2013, 6(2): 401-422. doi: 10.3934/dcdss.2013.6.401

## Asymptotic analysis for the 3D primitive equations in a channel

 1 The Institute for Scientific Computing and Applied Mathematics, Indiana University, 831 E. 3rd St., Rawles Hall, Bloomington, IN 47405, United States 2 School of Technology Management/ Mechanical, and Advanced Materials Engineering/ Natural Science, Ulsan National Institute of Science and Technology, San 194, Banyeon-ri, Eonyang-eup, Ulju-gun, Ulsan, South Korea

Received  July 2011 Revised  November 2011 Published  November 2012

In this article, we give an asymptotic expansion, with respect to the viscosity which is considered here to be small, of the solutions of the $3D$ linearized Primitive Equations (EPs) in a channel with lateral periodicity. A rigorous convergence result, in some physically relevant space, is proven. This allows, among other consequences, to confirm the natural choice of the non-local boundary conditions for the non-viscous PEs.
Citation: Makram Hamouda, Chang-Yeol Jung, Roger Temam. Asymptotic analysis for the 3D primitive equations in a channel. Discrete & Continuous Dynamical Systems - S, 2013, 6 (2) : 401-422. doi: 10.3934/dcdss.2013.6.401
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