Asymptotic analysis for the 3D primitive equations in a channel

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.

[1]  R. Temam,et al.  An interface problem: The two-layer shallow water equations , 2013 .

[2]  R. Temam,et al.  The one‐dimensional shallow water equations with transparent boundary conditions , 2011 .

[3]  Roger Temam,et al.  Boundary value problems for the shallow water equations with topography , 2011 .

[4]  R. Temam,et al.  Existence and uniqueness of solutions for the hydrostatic Euler equations on a bounded domain with analytic data , 2010 .

[5]  Roger Temam,et al.  Boundary layers for the 2D linearized primitive equations , 2008 .

[6]  R. Temam,et al.  The 3D Primitive Equations in the absence of viscosity : Boundary conditions and well-posedness in the linearized case , 2008 .

[7]  Jean-Pierre Raymond,et al.  Stokes and Navier-Stokes equations with nonhomogeneous boundary conditions , 2007 .

[8]  I. Kukavica,et al.  On the regularity of the primitive equations of the ocean , 2007 .

[9]  R. Temam,et al.  SOME SINGULAR PERTURBATION PROBLEMS RELATED TO THE NAVIER-STOKES EQUATIONS , 2007 .

[10]  G. Kobelkov,et al.  Existence of a solution ‘in the large’ for the 3D large-scale ocean dynamics equations , 2006 .

[11]  B. Desjardins,et al.  Mathematical Geophysics: An Introduction to Rotating Fluids and the Navier-Stokes Equations , 2006 .

[12]  R. Temam,et al.  Boundary conditions for the 2D linearized PEs of the ocean in the absence of viscosity , 2005 .

[13]  Chang-Yeol Jung,et al.  Numerical approximation of two‐dimensional convection‐diffusion equations with boundary layers , 2005 .

[14]  E. Titi,et al.  Global well-posedness of the three-dimensional viscous primitive equations of large scale ocean and atmosphere dynamics , 2005, math/0503028.

[15]  Roger Temam,et al.  Open Boundary Conditions for the Primitive and Boussinesq Equations , 2003 .

[16]  R. Temam,et al.  Boundary Layers Associated with Incompressible Navier–Stokes Equations: The Noncharacteristic Boundary Case , 2002 .

[17]  Marco Sammartino,et al.  Zero Viscosity Limit of the Oseen Equations in a Channel , 2001, SIAM J. Math. Anal..

[18]  R. Treadon,et al.  A Tutorial on Lateral Boundary Conditions as a Basic and Potentially Serious Limitation to Regional Numerical Weather Prediction , 1997 .

[19]  Roger Temam,et al.  On the equations of the large-scale ocean , 1992 .

[20]  J. Lions,et al.  New formulations of the primitive equations of atmosphere and applications , 1992 .

[21]  Shagi-Di Shih,et al.  Asymptotic anaylsis of a singular perturbation problem , 1987 .

[22]  J. Oliger,et al.  Theoretical and practical aspects of some initial-boundary value problems in fluid dynamics , 1976 .