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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.

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