Quasisimple Wave Solutions of Euler’s System of Equations for Ideal Gas

Abstract

Quasisimple wave solutions of Euler’s system of equations for ideal gas are investigated under the assumption of spherical and cylindrical symmetries. These solutions are proved to be stabilized into sound wave solutions and cavitation. It is proved that if initial conditions from outside the invariant region approach to transitional solution, then reciprocal of the self-similar parameter goes to infinity. However, when initial conditions stabilize into sound waves or cavitation, then reciprocal of self-similar parameter approaches finite value. Further, it is proved that initial conditions can be parametrized so that some of the initial conditions stabilize into sound wave solutions. The rest of the initial conditions are proved to be stabilized into cavitation. This extends the work of G. I. Taylor to the case of cavitation. It is proved that quasisimple wave solutions exist for the balance laws comprised of Euler’s system of equations in the case of cylindrically and spherically symmetric cases. The description applies to the motion of cylindrical and spherical piston in real life. In particular, self-similar description of appearance of vacuum in the motion of cylindrical and spherical piston is given.