WIAS Preprint No. 2871, (2021)

Differentiability properties for boundary control of fluid-structure interactions of linear elasticity with Navier--Stokes equations with mixed-boundary conditions in a channel



Authors

  • Hintermüller, Michael
    ORCID: 0000-0001-9471-2479
  • Kröner, Axel

2020 Mathematics Subject Classification

  • 74F10

Keywords

  • Fluid-structure interaction, boundary control, differentiability properties, Navier-Stokes equation, mixed boundary conditions, domains with corners

DOI

10.20347/WIAS.PREPRINT.2871

Abstract

In this paper we consider a fluid-structure interaction problem given by the steady Navier Stokes equations coupled with linear elasticity taken from [Lasiecka, Szulc, and Zochoswki, Nonl. Anal.: Real World Appl., 44, 2018]. An elastic body surrounded by a liquid in a rectangular domain is deformed by the flow which can be controlled by the Dirichlet boundary condition at the inlet. On the walls along the channel homogeneous Dirichlet boundary conditions and on the outflow boundary do-nothing conditions are prescribed. We recall existence results for the nonlinear system from that reference and analyze the control to state mapping generaziling the results of [Wollner and Wick, J. Math. Fluid Mech., 21, 2019] to the setting of the nonlinear Navier-Stokes equation for the fluid and the situation of mixed boundary conditions in a domain with corners.

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