Blow up and grazing collision in viscous fluid solid interaction systems. (English) Zbl 1187.35290

Hillairet, Matthieu; Takahashi, Takéo

Ann. Inst. Henri Poincaré, Anal. Non Linéaire 27, No. 1, 291-313 (2010).

Summary: 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.

MSC:

35R35	Free boundary problems for PDEs
76D03	Existence, uniqueness, and regularity theory for incompressible viscous fluids
76D05	Navier-Stokes equations for incompressible viscous fluids
35B44	Blow-up in context of PDEs
74F10	Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)

Keywords:

fluid-structure interaction; Navier-Stokes equations; rigid body; Cauchy theory; qualitative properties; collisions

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