Special Session 26: 

Weak-strong uniqueness for a fluid-rigid body interaction problem

Boris Muha
University of Zagreb
Croatia
Co-Author(s):    N. V. Chemetov and \\v S. Ne\\v casov\\`a
Abstract:
We consider a coupled PDE-ODE 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. To the best of our knowledge this is the first weak-strong uniqueness result in the area of fluid-structure interaction.