The compression problem of the polytropic gas bubble coated by the layer of an ideal incompressible liquid has been solved in the closed form. The simple algebraic formulae, which determine the velocity and pressure fields in the liquid layer, as well as the critical (minimal) radius of the maximally compressed bubble, have been derived. The adiabatic and isothermal gas compressions were examined. The time of the compression process was determined. The general solution of the problem was achieved. The solutions, known in the literature of the similar but simplified problems, result from our solution as particular cases.
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