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

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

Journal

Annals of Mathematics
ISSN: 0003-486X

Output data

Year: 2014, Pages: 769-807 Pages count : 39 DOI: 10.4007/annals.2015.181.2.7

Authors

Korobkov Mikhail ^1,2 , Pileckas Konstantin ³ , Russo Remigio ⁴

Affiliations

1	Sobolev Institute of Mathematics
2	Novosibirsk State University
3	Vilnius University
4	Department of Mathematics and Physics, Second University of Naples, Italy

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. (For axially symmetric domains, data is assumed to be axially symmetric as well.) 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.

Korobkov M. , Pileckas K. , Russo R.
Solution of Leray's problem for stationary Navier-Stokes equations in plane and axially symmetric spatial domains
Annals of Mathematics. 2014. P.769-807. DOI: 10.4007/annals.2015.181.2.7 WOS Scopus OpenAlex

Web of science:	WOS:000352017600007
Scopus:	2-s2.0-84912038838
OpenAlex:	W2962734697

DB	Citing
Scopus	53
OpenAlex	65
Web of science	49