Flow problem for the equations of an ideal fluid

One considers the problem of the flow of an ideal fluid through a bounded domain with prescribed velocity vector at the entry and prescribed pressure on the part of the outflow. One proves the solvability of the problem, locally with respect to time, in the case of a plane-parallel or axisymmetric motion.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova Akad. Nauk SSSR, Vol. 96, pp. 84–96, 1980.The authors express their sincere gratitude to O. A. Ladyzhenskaya for the helpful discussion of the results of the paper.