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.