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

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.


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.)
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