Mathematical Problems in Mechanics
The Navier–Stokes equations with Navier's boundary condition around moving bodies in presence of collisions
Comptes Rendus. Mathématique, Volume 347 (2009) no. 11-12, pp. 685-690.

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 C2 front surfaces in comparison with the no-slip Dirichlet condition.

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.

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DOI: 10.1016/j.crma.2009.03.021
Neustupa, Jiří 1; Penel, Patrick 2

1 Czech Technical University, Faculty of Mechanical Engineering, Department of Technical Mathematics, Karlovo nám. 13, 121 35 Praha 2, Czech Republic
2 Université du Sud Toulon-Var, département de mathématique et laboratoire systèmes navals complexes, BP 20132, 83957 La Garde, France
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Neustupa, Jiří; Penel, Patrick. The Navier–Stokes equations with Navier's boundary condition around moving bodies in presence of collisions. Comptes Rendus. Mathématique, Volume 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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