Abstract
A theorem is presented proving the unique solvability 'in the large' of the system of primitive equations on an arbitrary smooth oriented Riemannian manifold in a cylindrical domain. Namely, it is shown for an arbitrary interval of time , in the d domain , where and is a compactly embedded subdomain of a -manifold , for any viscosity coefficients and initial conditions , , and , there exists a unique generalized solution such that , ( is the vertical variable) and the norms and are continuous in .Bibliography: 12 titles.
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