The Coupled PDE System Arising in Fluid/Structure Interaction. Part I: Explicit Semigroup Generator and its Spectral Properties

摘要

A 2-d or 3-d fluid-structure interaction model in its linear form is considered This is, essentially, the model already discussed in the literature (eg , [D-G-H-L 1]), which couples on the interface the linear version of the Navier-Stokes equations with the equations of linear elasticity (wave-like) Several results are established, including: (i) well-posedness in the semigroup sense of the coupled structure, and its adjoint, on the natural energy space; (ii) a precise spectral analysis of the corresponding generators; (iii) related stability properties An unexpected and revealing result is that the spectrum of the generators on the imaginary axis is geometry-dependent.