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The 3D Primitive Equations in the absence of viscosity: Boundary conditions and well-posedness in the linearized case

By A. Rousseau, R. Temam and J. Tribbia

Abstract

AbstractIn this article we consider the 3D Primitive Equations (PEs) of the ocean, without viscosity and linearized around a stratified flow. As recalled in the Introduction, the PEs without viscosity ought to be supplemented with boundary conditions of a totally new type which must be nonlocal. In this article a set of boundary conditions is proposed for which we show that the linearized PEs are well-posed. The proposed boundary conditions are based on a suitable spectral decomposition of the unknown functions. Noteworthy is the rich structure of the Primitive Equations without viscosity. Our study is based on a modal decomposition in the vertical direction; in this decomposition, the first mode is essentially a (linearized) Euler flow, then a few modes correspond to a stationary problem partly elliptic and partly hyperbolic; finally all the other modes correspond to a stationary problem fully hyperbolic

Publisher: Elsevier Masson SAS.
Year: 2008
DOI identifier: 10.1016/j.matpur.2007.12.001
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