A No-Contact Result for a Plate-Fluid Interaction System in Dimension Three

Abstract.

We address the fluid-structure interaction between a viscous incompressible fluid and an elastic plate forming its moving upper boundary in three dimensions. The fluid is described by the incompressible Navier–Stokes equations with a free upper boundary that evolves according to the motion of the structure, coupled via the velocity- and stress-matching conditions. Under the natural energy bounds and additional regularity assumptions on the weak solutions, we prove a non-contact property with a uniform separation of the plate from the rigid boundary. The result does not require damping in the plate equation.