1302.0731 (Mikhail. V. Korobkov et al.)

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

Mikhail. V. Korobkov, Konstantin Pileckas, Remigio Russo

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

View original: http://arxiv.org/abs/1302.0731