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Group properties and new solutions of Navier-Stokes equations

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Summary

Using the machinery of Lie theory (groups and algebras) applied to the Navier-Stokes equations a number of exact solutions for the steady state are derived in (two) three dimensions. It is then shown how each of these generates an infinite number of time-dependent solutions via (three) four arbitrary functions of time. This algebraic structure also provides the mechanism to search for other solutions since its character is inferred from the basic equations.

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Author notes

  1. R. E. Boisvert

    Present address: M.I.T. Lincoln Laboratory, 02173, Lexington, MA, U.S.A.

Authors and Affiliations

  1. School of Mathematics, Georgia Institute of Technology, 30332, Atlanta, Georgia, U.S.A.

    R. E. Boisvert

  2. School of Mathematics, Georgia Institute of Technology, 30332, Atlanta, Georgia, U.S.A.

    W. F. Ames

  3. Department of Mathematics, India Institute of Technology, 36, Madras, India

    U. N. Srivastava

Authors
  1. R. E. Boisvert
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  2. W. F. Ames
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  3. U. N. Srivastava
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Additional information

This research was supported in part by U.S. Army Grant No. DAAG29-81-K-0042.

Research supported by the Alexander von Humboldt Foundation while in residence at the University of Karlsruhe, Federal Republic of Germany.

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Boisvert, R.E., Ames, W.F. & Srivastava, U.N. Group properties and new solutions of Navier-Stokes equations. J Eng Math 17, 203–221 (1983). https://doi.org/10.1007/BF00036717

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  • DOI: https://doi.org/10.1007/BF00036717

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