On the existence and uniqueness of solution to problems of fluid dynamics on a sphere

Orthogonal projectors and fractional derivatives on a two-dimensional unit sphere are introduced. Hilbert and Banach spaces of smooth functions on the sphere and some embedding assertions are given. The unique solvability of a nonstationary problem of vortex dynamics of viscous incompressible fluid on a rotating sphere is shown. The existence of a weak solution to stationary problem is proved too, and a condition guaranteeing the uniqueness of solution is also given.