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We consider the linear Primitive Equations of the ocean in the threedimensional space, with horizontal periodic and vertical Dirichlet boundaryconditions. Thanks to Fourier transforms we are able to calculate explicitlythe pressure term. We then state existence, unicity and regularity results forthe linear time-depending Primitive Equations, with low-regularity right-handside.

Regularity results for the Primitive Equations of the ocean