Discharge of ideal gas into vacuum

Three-dimensional nonisentropic flow of an ideal gas adjoining a vacuum or occurring upon instantaneous removal of a solid barrier which separates it from a vacuum is analyzed as a problem of decaying discontinuity. The solution to the corresponding system of three vector equations of motion and the equation of state, using the function sigma =sigma sub O(x)=p 1/2 (upsilon) (p-density of gas, upsilon 1), is sought in the form of special converging series. A convergence test reveals that the gas particles move along straight lines at constant velocity until infinite gradients of gas-dynamic parameters build up at the vacuum boundary. Four theorems are proved pertaining respectively to the existence of a unique analytical solution in the vicinity of the discontinuity surface, to its convergence region, to the constant velocity transient following the decay of the discontinuity, and to the corresponding Cauchy problem. The proof of the first theorem reduces to an analog of the proof of the Cauchy-Kowalewska theorem and it yields a lemma pertaining to the coefficients and exponents in the series.