Collisions in three-dimensional fluid structure interaction problems. (English) Zbl 1178.35291

Summary: This paper deals with a system composed of a rigid ball moving into a viscous incompressible fluid over a fixed horizontal plane. The equations of motion for the fluid are the Navier-Stokes equations, and the equations for the motion of the rigid ball are obtained by applying Newton’s laws. We show that for any weak solution of the corresponding system satisfying the energy inequality, the rigid ball never touches the plane. This result is the extension of that obtained in [the first author, Commun. Partial Differ. Equations 32, No. 9, 1345–1371 (2007; Zbl 1221.35279)] in the two-dimensional setting.


35Q30 Navier-Stokes equations
35R35 Free boundary problems for PDEs
76D03 Existence, uniqueness, and regularity theory for incompressible viscous fluids
76D05 Navier-Stokes equations for incompressible viscous fluids
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)


Zbl 1221.35279
Full Text: DOI HAL