Real processing IV. The derivation of the Navier–Stokes equation from the principle of minimal deformation

Abstract

As a special case of the general principle of minimal entropy production discussed in earlier parts of this series, we relate here the hydrodynamic Navier–Stokes equation including its non-linear term, to the minimisation of ∫∑ i( ∇v i) 2 dV , for fixed boundaries. The connection is made explicit for incompressible stationary flow; we shortly consider generalisations to the general pressure tensor, the non-stationary process, compressibility, and the principle of minimal entropy production.