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.
C. B. Millikan, On the steady motion of viscous, incompressible fluids; with particular reference to a variational principle, Phil. Mag. 7, 641–662 (1929)
V. Volterra, Theory of functionals and of integral and integro-differential equations, Blackie & Son Limited, London & Glasgow, 1931, p. 21
H. Lamb, Hydrodynamics, Dover Publications, New York, 1932, p. 580
A. Sommerfeld, Lectures on theoretical physics, Vol. II, Academic Press, 1964, p. 159
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
C. B. Millikan, On the steady motion of viscous, incompressible fluids; with particular reference to a variational principle, Phil. Mag. 7, 641–662 (1929)
V. Volterra, Theory of functionals and of integral and integro-differential equations, Blackie & Son Limited, London & Glasgow, 1931, p. 21
H. Lamb, Hydrodynamics, Dover Publications, New York, 1932, p. 580
A. Sommerfeld, Lectures on theoretical physics, Vol. II, Academic Press, 1964, p. 159
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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Article copyright:
© Copyright 1973
American Mathematical Society
