We study a 3D nonlinear moving boundary fluid-structure interaction problem describing the interaction of the fluid flow with a rigid body. The fluid flow is governed by 3D incompressible Navier-Stokes equations, while the motion of the rigid body is described by a system of ordinary differential equations called Euler equations for the rigid body. The equations are fully coupled via dynamical and kinematic coupling conditions. We consider two different kinds of kinematic coupling conditions: no-slip and slip. In both cases we prove a generalization of the well-known weak-strong uniqueness result for the Navier-Stokes equations to the fluid-rigid body system. More precisely, we prove that weak solutions that additionally satisfy Prodi-Serrin L r − L s condition are unique in the class of Leray-Hopf weak solutions. * The research of B.M. leading to these results has been supported by Croatian Science Foundation under the project IP-2018-01-3706† The research of Š.N. leading to these results has received funding from the Czech Sciences Foundation (GA ČR), 19-04243S and RVO 67985840.‡ The research of A.R. leading to these results has been supported by Croatian Science Foundation under the project IP-2018-01-3706, and by the Czech Sciences Foundation (GA ČR), 19-04243S and RVO 67985840.
We study a 3D fluid-rigid body interaction problem. The fluid flow is governed by 3D incompressible Navier-Stokes equations, while the motion of the rigid body is described by a system of ordinary differential equations describing conservation of linear and angular momentum. Our aim is to prove that any weak solution satisfying certain regularity conditions is smooth. This is a generalization of the classical result for the 3D incompressible Navier-Stokes equations, which says that a weak solution that additionally satisfy Prodi -Serrin L r − L s condition is smooth. We show that in the case of fluid -rigid body the Prodi -Serrin conditions imply W 2,p and W 1,p regularity for the fluid velocity and fluid pressure, respectively. Moreover, we show that solutions are C ∞ if additionally we assume that the rigid body acceleration is bounded almost anywhere in time variable. * The research of B.M. leading to these results has been supported by Croatian Science Foundation under the project IP-2018-01-3706† The research of Š.N. leading to these results has received funding from the Czech Sciences Foundation (GA ČR), 22-01591S. Moreover, Š. N. has been supported by Praemium Academiae of Š. Nečasová. CAS is supported by RVO:67985840.‡ The research of A.R. leading to these results has been supported by Croatian Science Foundation under the project IP-2019-04-1140. Moreover, The research of A.R. leading to these results has received funding from the Czech Sciences Foundation (GA ČR) 22-01591S, and by Praemium Academiae of Š. Nečasová.
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