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Abstract
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We consider a fluid-structure interaction system composed of a rigid ball immersed
into a viscous incompressible fluid. The motion of the structure satisfies the Newton
laws and the fluid equations are the standard Navier–Stokes system. At the boundary
of the fluid domain, we use the Tresca boundary conditions, that permit
the fluid to slip tangentially on the boundary under some conditions on
the stress tensor. More precisely, there is a threshold determining if the
fluid can slip or not and there is a friction force acting on the part where
the fluid can slip. Our main result is the existence of contact in finite time
between the ball and the exterior boundary of the fluid for this system in the
bidimensional case, in presence of gravity and in the case of a symmetric
configuration.
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Keywords
fluid-structure, Navier–Stokes system, Tresca boundary
conditions
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Mathematical Subject Classification 2010
Primary: 74F10
Secondary: 35Q30, 35R35, 76D05
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Milestones
Received: 19 December 2019
Revised: 6 May 2020
Accepted: 23 May 2020
Published: 13 May 2021
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