LXV. On the motion of a viscous fluid

Abstract

IT has been proved by Helmholtz and Korteweg that when the velocities at the boundary are given, the slow steady motion of an incompressible viscous liquid satisfies the condition of making F, the dissipation, an absolute minimum. If u0, v0, w0 be the velocities in one motion M0, and u, v, w those of another motion M satisfying the same boundary conditions, the difference of the two equations (1) will constitute a motion M' such that the boundary velocities vanish. If F0, F, F' denote the dissipatlon-functions for the three motions M0, M, M' respectively, all being of necessity positive, it is shown that more equations (2) ...