JournalsaihpcVol. 27, No. 1pp. 291–313

Blow up and grazing collision in viscous fluid solid interaction systems

  • Matthieu Hillairet

    IMT, Université Paul Sabatier Toulouse 3, 31062 Toulouse Cedex 9, France

  • Takéo Takahashi

    Institut Élie Cartan, UMR 7502, INRIA, Nancy-Université, CNRS, POB 239, Vandœuvre-lès-Nancy 54506, France, Team-project CORIDA, INRIA Nancy – Grand Est, France
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Abstract

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.

Cite this article

Matthieu Hillairet, Takéo Takahashi, Blow up and grazing collision in viscous fluid solid interaction systems. Ann. Inst. H. Poincaré Anal. Non Linéaire 27 (2010), no. 1, pp. 291–313

DOI 10.1016/J.ANIHPC.2009.09.007