Solution of Leray's problem for stationary Navier-Stokes equations in plane and axially symmetric spatial domains
Mathematical Physics
2013-02-05 v1 math.MP
Abstract
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.
Keywords
Cite
@article{arxiv.1302.0731,
title = {Solution of Leray's problem for stationary Navier-Stokes equations in plane and axially symmetric spatial domains},
author = {Mikhail. V. Korobkov and Konstantin Pileckas and Remigio Russo},
journal= {arXiv preprint arXiv:1302.0731},
year = {2013}
}
Comments
2 figures