Claudiu MINDRILA (Charles Univ., Prague)

Time-periodic weak solutions for an incompressible Newtonian fluid interacting with an elastic plate

Consider a smooth bounded 3D domain containing a Newtonian fluid which verifies the Navier-Stokes equations. To a flat part of this reference domain, an elastic membrane is attached and is allowed to move only in normal (vertical) direction. We assume that, on the boundary, the velocity of the fluid equals the velocity of the membrane. The system evolves under the action of external time-periodic forces. Provided that the magnitude of the forces and the volume of the domain remain sufficiently small, we prove that at least one time-periodic weak solution exists. This is a joint result with S. Schwarzacher (Univ. Uppsala & Charles Univ.) based on the paper “Time-periodic weak solutions for an incompressible Newtonian fluid interacting with an elastic plate” (SIAM J. on Math. Analysis, 2022.)