Weak-strong uniqueness for fluid-rigid body interaction problem with slip boundary condition. (English) Zbl 1406.76010
Summary: We consider a coupled partial differential equation-ordinary differential equation system describing the motion of the rigid body in a container filled with the incompressible, viscous fluid. The fluid and the rigid body are coupled via Navier’s slip boundary condition. We prove that the local in time strong solution is unique in the larger class of weak solutions on the interval of its existence. This is the first weak-strong uniqueness result in the area of fluid-structure interaction with a moving boundary.{
©2019 American Institute of Physics}
©2019 American Institute of Physics}
MSC:
| 76D05 | Navier-Stokes equations for incompressible viscous fluids |
| 35Q35 | PDEs in connection with fluid mechanics |
| 76D07 | Stokes and related (Oseen, etc.) flows |
| 35G60 | Boundary value problems for systems of nonlinear higher-order PDEs |
| 35D30 | Weak solutions to PDEs |
| 76D03 | Existence, uniqueness, and regularity theory for incompressible viscous fluids |
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