Boundary conditions for the 2D linearized PEs of the ocean in the absence of viscosity

A. Rousseau; Roger Temam; J. Tribbia

doi:10.3934/dcds.2005.13.1257

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2005, Volume 13, Issue 5: 1257-1276. Doi: 10.3934/dcds.2005.13.1257

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Boundary conditions for the 2D linearized PEs of the ocean in the absence of viscosity

1.
Laboratoire d'Analyse Numérique, Université Paris--Sud, Orsay
2.
The Institute for Scientific Computing and Applied Mathematics, Indiana University, 831 E. 3rd St., Rawles Hall, Bloomington, IN 47405
3.
National Center for Atmospheric Research, Boulder, Colorado

Received: November 30, 2004

Revised: April 30, 2005

Published: September 2005

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Abstract

The linearized Primitive Equations with vanishing viscosity are considered. Some new boundary conditions (of transparent type) are introduced in the context of a modal expansion of the solution which consist of an infinite sequence of integral equations. Applying the linear semi-group theory, existence and uniqueness of solutions is established. The case with nonhomogeneous boundary values, encountered in numerical simulations in limited domains, is also discussed.

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Mathematics Subject Classification: 35L50, 76N10, 47D06, 86A05.

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