Standard

Solutions symétriques du problème de Leray. / Pukhnachev, Vladislav.

In: Comptes Rendus Mathematique, Vol. 355, No. 1, 01.01.2017, p. 113-117.

Research output: Contribution to journal › Article › peer-review

Harvard

Pukhnachev, V 2017, 'Solutions symétriques du problème de Leray', Comptes Rendus Mathematique, vol. 355, no. 1, pp. 113-117. https://doi.org/10.1016/j.crma.2016.11.010

APA

Pukhnachev, V. (2017). Solutions symétriques du problème de Leray. Comptes Rendus Mathematique, 355(1), 113-117. https://doi.org/10.1016/j.crma.2016.11.010

Vancouver

Pukhnachev V. Solutions symétriques du problème de Leray. Comptes Rendus Mathematique. 2017 Jan 1;355(1):113-117. doi: 10.1016/j.crma.2016.11.010

Author

Pukhnachev, Vladislav. / Solutions symétriques du problème de Leray. In: Comptes Rendus Mathematique. 2017 ; Vol. 355, No. 1. pp. 113-117.

BibTeX

@article{bfd9fc14adb24f5a8e96a65247356508,
title = "Solutions sym{\'e}triques du probl{\`e}me de Leray",
abstract = "A stationary boundary-value problem for the Navier–Stokes equations of an incompressible fluid in a domain of a spherical layer type is considered. The velocity vector on the boundary is given. The solvability of this problem was proven by Jean Leray (1933) under an additional condition of a zero flux through each connected component of the flow domain boundary. The following problem is open up to now: does a solution to the flux problem exist if only the necessary condition of a zero total flux is satisfied? The present communication is devoted to the consideration of the Leray problem in a spherical-layer-type domain. An a priori estimate of the solution under the condition of flow symmetry with respect to a plane is obtained. This estimate implies the solvability of the problem.",
keywords = "NAVIER-STOKES EQUATIONS, EXISTENCE",
author = "Vladislav Pukhnachev",
year = "2017",
month = jan,
day = "1",
doi = "10.1016/j.crma.2016.11.010",
language = "французский",
volume = "355",
pages = "113--117",
journal = "Comptes Rendus Mathematique",
issn = "1631-073X",
publisher = "Elsevier",
number = "1",

}

RIS

TY - JOUR

T1 - Solutions symétriques du problème de Leray

AU - Pukhnachev, Vladislav

PY - 2017/1/1

Y1 - 2017/1/1

N2 - A stationary boundary-value problem for the Navier–Stokes equations of an incompressible fluid in a domain of a spherical layer type is considered. The velocity vector on the boundary is given. The solvability of this problem was proven by Jean Leray (1933) under an additional condition of a zero flux through each connected component of the flow domain boundary. The following problem is open up to now: does a solution to the flux problem exist if only the necessary condition of a zero total flux is satisfied? The present communication is devoted to the consideration of the Leray problem in a spherical-layer-type domain. An a priori estimate of the solution under the condition of flow symmetry with respect to a plane is obtained. This estimate implies the solvability of the problem.

AB - A stationary boundary-value problem for the Navier–Stokes equations of an incompressible fluid in a domain of a spherical layer type is considered. The velocity vector on the boundary is given. The solvability of this problem was proven by Jean Leray (1933) under an additional condition of a zero flux through each connected component of the flow domain boundary. The following problem is open up to now: does a solution to the flux problem exist if only the necessary condition of a zero total flux is satisfied? The present communication is devoted to the consideration of the Leray problem in a spherical-layer-type domain. An a priori estimate of the solution under the condition of flow symmetry with respect to a plane is obtained. This estimate implies the solvability of the problem.

KW - NAVIER-STOKES EQUATIONS

KW - EXISTENCE

UR - http://www.scopus.com/inward/record.url?scp=85007418018&partnerID=8YFLogxK

U2 - 10.1016/j.crma.2016.11.010

DO - 10.1016/j.crma.2016.11.010

M3 - статья

AN - SCOPUS:85007418018

VL - 355

SP - 113

EP - 117

JO - Comptes Rendus Mathematique

JF - Comptes Rendus Mathematique

SN - 1631-073X

IS - 1

ER -

ID: 9029163