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We study the nonhomogeneous boundary value problem for the Navier-Stokesequations of steady motion of a viscous incompressible fluid in arbitrarybounded multiply connected plane or axially-symmetric spatial domains. We provethat this problem has a solution under the sole necessary condition of zerototal flux through the boundary. The problem was formulated by Jean Leray 80years ago. The proof of the main result uses Bernoulli's law for a weaksolution to the Euler equations.

Solution of Leray's problem for stationary Navier-Stokes equations in plane and axially symmetric spatial domains