Existence of strong solutions to a fluid-structure system with a structure given by a finite number of parameters

Delay, Guillaume

ESAIM: Mathematical Modelling and Numerical Analysis , Tome 54 (2020) no. 1, pp. 301-333.

Suite au passage du modèle économique de la revue en S20, le texte intégral des articles des années 2019 et 2020 est accessible uniquement sur le site de l'éditeur et est réservé aux abonnés.

We study the existence of strong solutions to a 2d fluid-structure system. The fluid is modelled by the incompressible Navier–Stokes equations. The structure represents a steering gear and is described by two parameters corresponding to angles of deformation. Its equations are derived from a virtual work principle. The global domain represents a wind tunnel and imposes mixed boundary conditions to the fluid velocity. Our method reposes on the analysis of the linearized system. Under a compatibility condition on the initial data, we can guarantee local existence in time of strong solutions to the fluid-structure problem.

Classification : 74F10, 74H20, 74H25, 74H30, 76D03
Mots-clés : Strong solutions, fluid-structure interaction, Navier–Stokes equations, deformable structure

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