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. 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 inflnite 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.

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