Shock waves in arbitrary fluids

TLDR: In this article, the authors investigated the general hydrodynamical and thermodynamic foundations of the shock phenomenon and showed that the initial state and final state of a fluid are singular points for the differential equations of the fluid's shock layer.

Abstract: The following investigation tries to clear up the general hydrodynamical and thermodynamical foundations of the shock phenomenon.1 The first part, Sections 2–5, answers the question: What are the conditions for the equation of state of a fluid under which shocks with their distinctive qualitative features may be produced. These conditions, enumerated in Section 3, are partly of differential, partly of global nature. The second part, Sections 6–7, investigates the physical structure of the shock layer whose “infinitesimal” width is of the order of magnitude e provided heat conductivity and viscosity are small of the same order. Initial state and final state are singular points for the differential equations of the shock layer, and it is shown that they are of such a nature as to make one expect the problem to have a unique solution.