Solutions of the stationary Navier-Stokes system of equations with an infinite Dirichlet integral

In unbounded domains of the three-dimensional Euclidean space, having several exits _i at infinity of a sufficiently general form, one finds the solutions of the stationary Navier-Stokes system, equal to zero on the boundary of the domain , having arbitrary flow rates d_i through each exit _i, i=1,..., , and having an unbounded Dirichlet integral . One gives sufficient conditions for the existence of a solution.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 115, pp. 251–263, 1982.