On the existence and uniqueness of solution to problems of fluid dynamics on a sphere |
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Authors: | Yuri N Skiba |
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Institution: | Centro de Ciencias de la Atmósfera, Universidad Nacional Autónoma de México, Av. Universidad # 3000, Ciudad Universitaria, C.P. 04510, México, D.F., Mexico |
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Abstract: | 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. |
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