Improved boundary regularity for a Stokes-Lamé system

Francesca Bucci

doi:10.3934/eect.2021018

Article Contents

2022, Volume 11, Issue 1: 325-346. Doi: 10.3934/eect.2021018

This issue Previous Article Internal control for a non-local Schrödinger equation involving the fractional Laplace operator Next Article

Improved boundary regularity for a Stokes-Lamé system

Francesca Bucci

Università degli Studi di Firenze, Dipartimento di Matematica e Informatica, 50139 Firenze, Italy

Received: July 2020

Revised: January 2021

Early access: April 2021

Published: February 2022

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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.

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Mathematics Subject Classification: Primary: 35B65, 35Q74, 35Q93; Secondary: 49N10.

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