Blow up and grazing collision in viscous fluid solid interaction systems
Annales de l'I.H.P. Analyse non linéaire, Volume 27 (2010) no. 1, pp. 291-313.

We investigate qualitative properties of strong solutions to a classical system describing the fall of a rigid ball under the action of gravity inside a bounded cavity filled with a viscous incompressible fluid. We prove contact between the ball and the boundary of the cavity implies blow up of strong solutions and such a contact has to occur in finite time under symmetry assumptions on the initial data.

DOI: 10.1016/j.anihpc.2009.09.007
Classification: 35R35,  76D03,  76D05
Keywords: Fluid–structure interaction, Navier–Stokes equations, Rigid body, Cauchy theory, Qualitative properties, Collisions
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Hillairet, Matthieu; Takahashi, Takéo. Blow up and grazing collision in viscous fluid solid interaction systems. Annales de l'I.H.P. Analyse non linéaire, Volume 27 (2010) no. 1, pp. 291-313. doi : 10.1016/j.anihpc.2009.09.007. http://archive.numdam.org/articles/10.1016/j.anihpc.2009.09.007/

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