Stability of the adiabatic compression of an ideal gas by a thin shell

A new solution has been obtained for the problems of the isentropic compression of an ideal gas in the centered wave formulated in the Lagrangian variables. The developed method makes it possible in a single, uniform way to find the solution to the gas-dynamic problem in the plane, cylindrical, and spherical cases for an initially uniform motionless gas. Equations were derived describing the evolution of the small perturbations of the shell in the case where the acceleration is time-dependent. The shell is assumed to be thin and structureless, and its mass is supposed to exceed significantly the mass of the gas surrounding the shell. The cases of the planar, cylindrical, and spherical geometries of the system are considered. The stability of the shell’s motion producing isentropic compression of the gas is considered with respect to the evolution of small perturbations of plane-wave and angularharmonic types. It is shown that under the isentropic compression of a gas, the increase in the shell’s perturbations of the plane-wave type is limited both in the planar and cylindrical geometries. The limiting growth in the amplitude of such perturbations is calculated. The increase in the perturbations of the angular-harmonic type is demonstrated to be unlimited both in cylindrical and in spherical geometries. The increment in the growth of such perturbations has been calculated.