[Équations de Navier–Stokes avec conditions aux limites de Navier pour décrire un fluide autour de corps en mouvement pouvant entrer en collision]
Dans cette Note, nous considérons les équations de Navier–Stokes avec des conditions aux limites de Navier dans un domaine borné temporellement variable contenant un nombre fini de corps compacts en mouvement. Le mouvement de ces corps est supposé connu, ainsi que la simulation de leurs contacts ou collisions éventuels (en nombre fini, entre eux ou avec la frontière du domaine). Nous établissons un résultat d'existence, globale en temps, des solutions faibles. Le choix des conditions aux limites est intéressant à commenter par comparaison avec les conditions standard de Dirichlet.
In this Note, we treat the Navier–Stokes equation with slip Navier's boundary condition in a time variable domain around a finite system of compact bodies moving in a container. The motion of the bodies is assumed to be a priori known. The bodies may collide at a finite number of time instants. We present the theorem on the global in time existence of a weak solution. It is remarkable that Navier's boundary condition enables us to consider a larger class of possible collisions of bodies with front surfaces in comparison with the no-slip Dirichlet condition.
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@article{CRMATH_2009__347_11-12_685_0,
author = {Neustupa, Ji\v{r}{\'\i} and Penel, Patrick},
title = {The {Navier{\textendash}Stokes} equations with {Navier's} boundary condition around moving bodies in presence of collisions},
journal = {Comptes Rendus. Math\'ematique},
pages = {685--690},
publisher = {Elsevier},
volume = {347},
number = {11-12},
year = {2009},
doi = {10.1016/j.crma.2009.03.021},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2009.03.021/}
}
TY - JOUR AU - Neustupa, Jiří AU - Penel, Patrick TI - The Navier–Stokes equations with Navier's boundary condition around moving bodies in presence of collisions JO - Comptes Rendus. Mathématique PY - 2009 SP - 685 EP - 690 VL - 347 IS - 11-12 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2009.03.021/ DO - 10.1016/j.crma.2009.03.021 LA - en ID - CRMATH_2009__347_11-12_685_0 ER -
%0 Journal Article %A Neustupa, Jiří %A Penel, Patrick %T The Navier–Stokes equations with Navier's boundary condition around moving bodies in presence of collisions %J Comptes Rendus. Mathématique %D 2009 %P 685-690 %V 347 %N 11-12 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2009.03.021/ %R 10.1016/j.crma.2009.03.021 %G en %F CRMATH_2009__347_11-12_685_0
Neustupa, Jiří; Penel, Patrick. The Navier–Stokes equations with Navier's boundary condition around moving bodies in presence of collisions. Comptes Rendus. Mathématique, Tome 347 (2009) no. 11-12, pp. 685-690. doi : 10.1016/j.crma.2009.03.021. http://www.numdam.org/articles/10.1016/j.crma.2009.03.021/
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