Abstract
The work researches the evolution of the free surface which limits the polytropic, isentropic and self-gravitating ideal gas moving in vacuum. Gas currents are described with the mathematical model of gas dynamics, constructed due to the system of nonlinear integro-differential equations, expressed in Euler coordinate system. The transformation of the given system to the Lagrangian coordinates lets reduce it to the equivalent system consisting of integral Voltair’s equations and the equation of continuity in the Lagrangian form, and also it lets break down the unknown boundaries. Free boundary is determined as a great number of points of the system of integral equations solution achieved when depicting the boundary points of the initial area within the point of the moving area. For the system there is the proved theorem of the existence and uniqueness of the solution of the Cauchy problem in the space of the infinitely differentiated functions. Methods of qualitative research of the system of gas dynamics were applied in the work for the research of the evolution of the free surface.
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