Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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On the connection between the elliptic equations of the Navier-Stokes type and the theory of harmonic functionals


Author: S. M. Deshpande
Journal: Quart. Appl. Math. 31 (1973), 43-52
MSC: Primary 76.49
DOI: https://doi.org/10.1090/qam/431929
MathSciNet review: 431929
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Abstract: It is established in this paper, under conditions more general than those used by Millikan, that the two-dimensional incompressible viscous flows past finite bodies cannot be equivalent to a variational problem of the Euler-Lagrange type. It has thereby been possible to obtain two harmonic functionals with a close relation to the Navier-Stokes equations.


References [Enhancements On Off] (What's this?)

  • [1] C. B. Millikan, On the steady motion of viscous, incompressible fluids; with particular reference to a variational principle, Phil. Mag. 7, 641-662 (1929)
  • [2] V. Volterra, Theory of functionals and of integral and integro-differential equations, Blackie & Son Limited, London & Glasgow, 1931, p. 21
  • [3] H. Lamb, Hydrodynamics, Dover Publications, New York, 1932, p. 580
  • [4] A. Sommerfeld, Lectures on theoretical physics, Vol. II, Academic Press, 1964, p. 159
  • [5] S. M. Deshpande, Variational formulation of Navier-Stokes equations in complex function space, Department of Aeronautical Engineering, Indian Institute of Science, Bangalore, Rep. 71 FM 10, 1971

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DOI: https://doi.org/10.1090/qam/431929
Article copyright: © Copyright 1973 American Mathematical Society


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