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, p. 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 : https://doi.org/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
@article{AIHPC_2010__27_1_291_0,
author = {Hillairet, Matthieu and Takahashi, Tak\'eo},
title = {Blow up and grazing collision in viscous fluid solid interaction systems},
journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
publisher = {Elsevier},
volume = {27},
number = {1},
year = {2010},
pages = {291-313},
doi = {10.1016/j.anihpc.2009.09.007},
zbl = {1187.35290},
mrnumber = {2580511},
language = {en},
url = {http://www.numdam.org/item/AIHPC_2010__27_1_291_0}
}

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://www.numdam.org/item/AIHPC_2010__27_1_291_0/

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