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October  2005, 13(5): 1257-1276. doi: 10.3934/dcds.2005.13.1257

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

A. Rousseau 1, , Roger Temam 2, and  J. Tribbia 3,

1. 

Laboratoire d'Analyse Numérique, Université Paris--Sud, Orsay, France
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, United States

Received  December 2004 Revised  May 2005 Published  September 2005

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.
Keywords: Nonviscous Primitive Equations, limited domains, well-posedness, transparent boundary conditions, semi-group theory.
Mathematics Subject Classification: 35L50, 76N10, 47D06, 86A0.
Citation: A. Rousseau, Roger Temam, J. Tribbia. Boundary conditions for the 2D linearized PEs of the ocean in the absence of viscosity. Discrete and Continuous Dynamical Systems, 2005, 13 (5) : 1257-1276. doi: 10.3934/dcds.2005.13.1257
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