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On the regularity of the primitive equations of the ocean. (English) Zbl 1136.35069

Summary: We prove the existence of global strong solutions of the primitive equations of the ocean in the case of the Dirichlet boundary conditions on the side and the bottom boundaries including the varying bottom topography. Previously, the existence of global strong solutions was known in the case of the Neumann boundary conditions in a cylindrical domain [C. Cao and E. S. Titi, Ann. Math. (2) 166, No. 1, 245–267 (2007; Zbl 1151.35074)].

MSC:

35Q30 Navier-Stokes equations
76B03 Existence, uniqueness, and regularity theory for incompressible inviscid fluids

Citations:

Zbl 1151.35074
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