Geodesic
Boundary value problems for equations of viscous heat-conducting gas in time-increasing non-cylindrical domains
Ufa mathematical journal, Tome 6 (2014) no. 4, pp. 81-98

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In this paper we prove the global solvability of the initial-boundary value problems for the complete system of equations describing one-dimensional non-stationary flow of the viscous heat-conducting gas in time-increasing non-cylindrical domains. Local existence and uniqueness of these problems are proved in earlier articles by Kazhikhov A. V. and Kaliev I. A. This is why, the proof of the global in time existence and uniqueness theorem is connected with obtaining a priori estimates, in which the constant depend only on the data of the problem and the value of the time interval $T$, but do not depend on the period of existence of a local solution. The study is made in terms of Eulerian variables.
Keywords: Navier–Stokes equations system, heat-conducting gas, global solvability, time-increasing non-cylindrical domains. 
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     title = {Boundary value problems for equations of viscous heat-conducting gas in time-increasing non-cylindrical domains},
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I. A. Kaliev; A. A. Shukhardin; G. S. Sabitova. Boundary value problems for equations of viscous heat-conducting gas in time-increasing non-cylindrical domains. Ufa mathematical journal, Tome 6 (2014) no. 4, pp. 81-98. http://geodesic.mathdoc.fr/item/UFA_2014_6_4_a6/