On the possibility of improving classic hydrodynamics equations by an increase in the number of hydrodynamic values

Abstract

Any of the infinite number of invariants of a binary collision of structureless particles was shown to annihilate the collision integral written in the 12-dimensional phase space of two particles. Its own principal hydrodynamic value corresponds to each of these invariants. The six-dimensional phase space of one particle can only accommodate three lower binary collision invariants that allow the integral of collisions to be annihilated. The first equation of the Bogolybov-Born-Green-Kirkwood-Yvon hierarchy is, however, not closed, and the transition from the 6-dimensional phase space to the hydrodynamic stage of description is therefore closed. The Boltzmann hypothesis closes the kinetic equation and therefore opens up the possibility of approximate transition to hydrodynamics. Just the Boltzmann hypothesis allows classic hydrodynamics equations constructed with the use of only three lower principal hydrodynamic values to be substantiated statistically. It should be expected that the neglect of the higher principal hydrodynamic values will limit the applicability range of classic hydrodynamics to states insignificantly removed from the statistical equilibrium state. Most probably, just this limitation is responsible for obvious discrepancy between the results of direct numerical integration of the Navier-Stokes equation and the experimental data on flows that lost stability. The possibility of the improvement of classic hydrodynamics equations is sought on the way toward an increase in the number of principal hydrodynamic values.