A process of axisymmetric unlimited shock-free compression of a perfect gas

Using Sidorov's ideas and analytical methods for solving the problem of the shock-free compression of a gas acted upon by a piston, a new parameterc form of the solution of the equation for the self-similar velocity potential of a gas is proposed. This enables the problem of constructing the flow with an unlimited increase in the gas-dynamic parameters to be reduced to solving the Cauchy problem for a single ordinary differential equation with a bounded integration interval. The solution of the gas-dynamic equations thus obtained may be of interest in constructing the process of unlimited compression of a perfect gas, at rest at the initial instant of time inside a solid of revolution of the “plate” type, and its describes the gas flow in a certain part of the compressed volume. Asymptotic estimates of the gas-dynamic quantities are established analytically.