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We show weak-strong uniqueness and stability results for the motion of a twoor three dimensional fluid governed by the Navier-Stokes equation interactingwith a flexible, elastic plate of Koiter type. The plate is situated at the topof the fluid and as such determines the variable part of a time changing domain(that is hence a part of the solution) containing the fluid. The uniquenessresult is a consequence of a stability estimate where the difference of twosolutions is estimated by the distance of the initial values and outer forces.For that we introduce a methodology that overcomes the problem that the two(variable in time) domains of the fluid velocities and pressures are not thesame. The estimate holds under the assumption that one of the two weaksolutions possesses some additional higher regularity. The additionalregularity is exclusively requested for the velocity of one of the solutionsresembling the celebrated Ladyzhenskaya-Prodi-Serrin conditions in the givenframework.

Weak-strong uniqueness for an elastic plate interacting with the Navier Stokes equation