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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References
Arnold, V. I.: Sur la geometrie differentielle des groupes de Lie. Ann. Inst. Fourier (Grenoble) 16 (1966) 1, 319–361.
Chorin, A. J.; Hughes, T.; McCracken, M.; Marsden, J.: Product formulas and numerical algorithms. Comm. Pure Appl. Math. 31 (1978), 205–257.
Ebin, D. G.: The manifolds of riemannian metrics. Bull. Amer. Math. Soc. 74 (1968), 1002–1004.
Ebin, D. G.; Marsden, J.: Groups of diffeomorphisms and the motion of an incompressible fluid. Ann. of Math. 92 (1970), 102–163.
Elworthy, K. D.: Stochastic differential equations on manifolds. LMS Lecture Note 70, N. Y., Cambridge Univ. Press (1982).
Klingenberg, W.: Riemannian geometry. Berlin, N. Y., De Gruyter (1982).
Kobayashi, S.; Nomizu, K.: Foundations of differential geometry I. Interscience Pub. (1969).
Ladyzhenskaya, O.: The mathematical theory of viscous incompressible flow. Gordon and Breach, N. Y., 2nd edition (1969).
Marsden, J.: Applications of global analysis in mathematical physics. Publish or Perish, Boston (1974).
Palais, R.: Foundations of global nonlinear analysis. Benjamin, N. Y., (1968).
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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