Regularity of boundary traces for a fluid-solid interaction model

Francesca Bucci; Irena Lasiecka

doi:10.3934/dcdss.2011.4.505

Article Contents

2011, Volume 4, Issue 3: 505-521. Doi: 10.3934/dcdss.2011.4.505

This issue Previous Article Preface Next Article Complete abstract differential equations of elliptic type with general Robin boundary conditions, in UMD spaces

Regularity of boundary traces for a fluid-solid interaction model

Francesca Bucci^1, and
Irena Lasiecka^2,

1.
Università degli Studi di Firenze, Dipartimento di Matematica Applicata, Via S. Marta 3, 50139 Firenze
2.
Department of Mathematics, University of Virginia, Charlottesville, VA 22904

Received: April 30, 2009

Revised: November 30, 2009

Published: May 2011

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Abstract

We consider a mathematical model for the interactions of an elastic body fully immersed in a viscous, incompressible fluid. The corresponding composite PDE system comprises a linearized Navier-Stokes system and a dynamic system of elasticity; the coupling takes place on the interface between the two regions occupied by the fluid and the solid, respectively. We specifically study the regularity of boundary traces (on the interface) for the fluid velocity field. The obtained trace regularity theory for the fluid component of the system-of interest in its own right-establishes, in addition, solvability of the associated optimal (quadratic) control problems on a finite time interval, along with well-posedness of the corresponding operator Differential Riccati equations. These results complement the recent advances in the PDE analysis and control of the Stokes-Lamé system.

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Mathematics Subject Classification: 74F10, 35B65, 35B37 (35Q93); 49J20, 49N10.

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