On the possibility of gasdynamic effects at the critical point of the phase equilibrium: PMM Vol. 37, N°1, 1973, pp. 169–171

Abstract

A possibility is indicated of appearance of density excursions in one-dimensional unsteady fluid flows near the critical point of the phase equilibrium, resulting from the singularities in the equation of state. The present investigations are concerned with the question, whether the classical solutions of the problem and the initial conditions for the one-dimensional unsteady gasdynamic equations can become infinite in the nonisoentropic case. Here we have to consider a system of three quasilinear hyperbolic equations which, as we know [1, 2], usually have unbounded solutions. On the other hand, the system of gasdynamic equations has a number of specific properties. Of those the most important is the presence of a single invariant, i.e. of a function which remains bounded [1]. Another important property consists of the fact that the generalized Riemann invariants satisfy multi-dimensional integral equations of Volterra type, in which the cone of integration is represented by the domain of definition of the hyperbolic equations and the boundedness of the solution follows from the fine properties of the integrability of the kernel. In the terms of the gasdynamic equations the latter lead to restrictions imposed on the equations of state. The properties themselves follow from the boundedness of the variation of entropy along the sonic characteristics and from the weak linearity (tangency) of the entropic characteristics [3].