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.
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}, 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://archive.numdam.org/articles/10.1016/j.anihpc.2009.09.007/} }
TY - JOUR AU - Hillairet, Matthieu AU - Takahashi, Takéo TI - Blow up and grazing collision in viscous fluid solid interaction systems JO - Annales de l'I.H.P. Analyse non linéaire PY - 2010 SP - 291 EP - 313 VL - 27 IS - 1 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.anihpc.2009.09.007/ DO - 10.1016/j.anihpc.2009.09.007 LA - en ID - AIHPC_2010__27_1_291_0 ER -
%0 Journal Article %A Hillairet, Matthieu %A Takahashi, Takéo %T Blow up and grazing collision in viscous fluid solid interaction systems %J Annales de l'I.H.P. Analyse non linéaire %D 2010 %P 291-313 %V 27 %N 1 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.anihpc.2009.09.007/ %R 10.1016/j.anihpc.2009.09.007 %G en %F 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://archive.numdam.org/articles/10.1016/j.anihpc.2009.09.007/
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