Existence 'in the large' of a solution to the system of equations of large-scale ocean dynamics on a manifold

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 [0,T], in the 3d domain Ω≡Ω'×[-h,0], where h=const and Ω' is a compactly embedded subdomain of a 2-manifold M, for any viscosity coefficients μ,ν,μ1,ν1>0 and initial conditions u0 element of W22(Ω), ∫-h0divu0 dz=0, and ρ0 element of W22(Ω), there exists a unique generalized solution such that ∂zu element of W21(QT), ∂zρ element of W21(QT) (z is the vertical variable). Bibliography: 12 titles.