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January  2009, 8(1): 335-359. doi: 10.3934/cpaa.2009.8.335

Boundary layers for the 2D linearized primitive equations

Makram Hamouda 1, , Chang-Yeol Jung 2, and  Roger Temam 3,

1. 

Faculty of Sciences of Bizerte, Department of Mathematics,7021 Zarzouna, Bizerte, Tunisia, The Institute for Scientific Computing and Applied Mathematics, Indiana University, 831 E. 3rd St., Rawles Hall, Bloomington, IN 47405, United States
2. 

Department of Mathematics, Arizona State University,Tempe, AZ 85287-1804, 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, 831 E. 3rd St., Rawles Hall, Bloomington, IN 47405

Received  July 2008 Revised  September 2008 Published  October 2008

In this article, we establish the asymptotic behavior, when the viscosity goes to zero, of the solutions of the Linearized Primitive Equations (LPEs) in space dimension $2$. More precisely, we prove that the LPEs solution behaves like the corresponding inviscid problem solution inside the domain plus an explicit corrector function in the neighborhood of some parts of the boundary. Two cases are considered, the subcritical and supercritical modes depending on the fact that the frequency mode is less or greater than the ratio between the reference stratified flow (around which we linearized) and the buoyancy frequency. The problem of boundary layers for the LPEs is of a new type since the corresponding limit problem displays a set of (unusual) nonlocal boundary conditions.
Keywords: Primitive equations, boundary layers, singular perturbation analysis.
Mathematics Subject Classification: 35L50, 47D06, 76D10, 86A05.
Citation: Makram Hamouda, Chang-Yeol Jung, Roger Temam. Boundary layers for the 2D linearized primitive equations. Communications on Pure & Applied Analysis, 2009, 8 (1) : 335-359. doi: 10.3934/cpaa.2009.8.335
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