The nonhomogeneous boundary value problem for the steady Navier–Stokes equations is studied in a three-dimensional axially symmetric bounded domain with multiply connected Lipschitz boundary. We assume that the boundary value is axially symmetric. Our results imply, in particular, the existence of the solution with arbitrary large fluxes over the connected components of the boundary, provided that all these components intersect the axis of the symmetry. The proof uses the Bernoulli law for a weak solution to the Euler equations and the one-side maximum principle for the total head pressure corresponding to this solution.
Des conditions aux limites non-homogènes des équations de Navier–Stokes sont étudiées dans une région bornée tridimensionnelle ayant symétrie axiale et la frontière multiplement connexe. En particulier, dans le cas où toutes les composantes connexes de la frontière intersectent lʼaxe de symétrie, les résultats obtenus impliquent lʼexistence dʼune solution pour flux arbitrairement grands. La démonstration est basée sur la loi de Bernoulli pour la solution faible des équations dʼEuler et sur le principe de maximum pour la fonction de Bernoulli correspondante à cette solution.
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Keywords: Mécanique des fluides, Équations de Navier–Stokes
Mikhail Korobkov 1; Konstantin Pileckas 2; Remigio Russo 3
@article{CRMECA_2012__340_3_115_0,
author = {Mikhail Korobkov and Konstantin Pileckas and Remigio Russo},
title = {Steady {Navier{\textendash}Stokes} system with nonhomogeneous boundary conditions in the axially symmetric case},
journal = {Comptes Rendus. M\'ecanique},
pages = {115--119},
publisher = {Elsevier},
volume = {340},
number = {3},
year = {2012},
doi = {10.1016/j.crme.2012.01.001},
language = {en},
}
TY - JOUR AU - Mikhail Korobkov AU - Konstantin Pileckas AU - Remigio Russo TI - Steady Navier–Stokes system with nonhomogeneous boundary conditions in the axially symmetric case JO - Comptes Rendus. Mécanique PY - 2012 SP - 115 EP - 119 VL - 340 IS - 3 PB - Elsevier DO - 10.1016/j.crme.2012.01.001 LA - en ID - CRMECA_2012__340_3_115_0 ER -
%0 Journal Article %A Mikhail Korobkov %A Konstantin Pileckas %A Remigio Russo %T Steady Navier–Stokes system with nonhomogeneous boundary conditions in the axially symmetric case %J Comptes Rendus. Mécanique %D 2012 %P 115-119 %V 340 %N 3 %I Elsevier %R 10.1016/j.crme.2012.01.001 %G en %F CRMECA_2012__340_3_115_0
Mikhail Korobkov; Konstantin Pileckas; Remigio Russo. Steady Navier–Stokes system with nonhomogeneous boundary conditions in the axially symmetric case. Comptes Rendus. Mécanique, Volume 340 (2012) no. 3, pp. 115-119. doi : 10.1016/j.crme.2012.01.001. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2012.01.001/
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