Improved boundary regularity for a Stokes-Lamé system

Abstract: This paper recalls a partial differential equations system, which is the linearization of a recognized fluid-elasticity interaction three-dimensional model. A collection of regularity results for the traces of the fluid variable on the interface between the body and the fluid is established, in the case a suitable boundary dissipation is present. These regularity estimates are geared toward ensuring the well-posedness of the Riccati equations which arise from the associated optimal boundary control problems on a finite as well as infinite time horizon. The theory of operator semigroups and interpolation provide the main tools.