Abstract
Following Ebin and Marsden the Navier-Stokes equation is viewed as a perturbation of a geodesic flow on the group of volume preserving diffeomorphisms on a compact Riemannian manifold. Existence and uniqueness of bounded solutions for all position time is shown by taking a higher order diffusion term.
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Communicated by D. Ferus
Partial y supported by Alexander von Humboldt Foundation
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Carverhill, A., Pedit, F.J. Global solutions of the Navier-Stokes equation with strong viscosity. Ann Glob Anal Geom 10, 255–261 (1992). https://doi.org/10.1007/BF00136868
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DOI: https://doi.org/10.1007/BF00136868