no. 1
Blow up and grazing collision in viscous fluid solid interaction systems
Annales de l'I.H.P. Analyse non linéaire, Tome 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
Mots clés : Fluid–structure interaction, Navier–Stokes equations, Rigid body, Cauchy theory, Qualitative properties, Collisions 
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     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},
     pages = {291--313},
     publisher = {Elsevier},
     volume = {27},
     number = {1},
     year = {2010},
     doi = {10.1016/j.anihpc.2009.09.007},
     mrnumber = {2580511},
     zbl = {1187.35290},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.anihpc.2009.09.007/}
}
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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, Tome 27 (2010) no. 1, pp. 291-313. doi : 10.1016/j.anihpc.2009.09.007. http://www.numdam.org/articles/10.1016/j.anihpc.2009.09.007/

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