The Navier–Stokes equations with Navier's boundary condition around moving bodies in presence of collisions

Abstract

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 C 2 front surfaces in comparison with the no-slip Dirichlet condition. To cite this article: J. Neustupa, P. Penel, C. R. Acad. Sci. Paris, Ser. I 347 (2009).