Improved boundary regularity for a Stokes-Lam\'e system

TL;DR

This paper establishes enhanced boundary regularity results for a linearized fluid-elasticity PDE system, facilitating the well-posedness of related optimal control problems through advanced mathematical tools.

Contribution

It introduces new boundary regularity estimates for the Stokes-Lamé system with boundary dissipation, aiding control theory applications.

Findings

Regularity results for fluid variable traces on the interface

Boundary dissipation improves trace regularity

Supports well-posedness of algebraic Riccati equations

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 -- in time and space, of local and global nature -- are geared toward ensuring the well-posedness of the algebraic Riccati equations which arise from the associated optimal boundary control problems on an infinite time horizon. The theory of operator semigroups and interpolation provide the main tools.