Linear parabolic-hyperbolic fluid-structure interaction models. The case of static interface

Abstract

The present exposition is focused on a well-established linear fluid-structure interaction model in the physical dimensions d = 2, 3. In [19] one finds a historical description of the fluid-structure problems, an extensive list of references up to 2003, and on enlightening physical discussion regarding the use of the static fluid-solid interface. In particular, it is argued in [19] that this case is a good mathematical model for small rapid oscillations of the structure. Moreover, such case provides important mathematical insight and thus serves as an enlightening first step toward two subsequent more general settings: (i) the model with the full (non-linear) Navier-Stokes fluid component and still static interface [13], [14], [30], [31], [32], [45] and (ii) the case of moving structure within the fluid.