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Existence of Weak Solutions for the Unsteady Interaction of a Viscous Fluid with an Elastic Plate

Chambolle, Antonin; Desjardins, Benoît; Esteban, Maria J.; Grandmont, Céline (2005), Existence of Weak Solutions for the Unsteady Interaction of a Viscous Fluid with an Elastic Plate, Journal of Mathematical Fluid Mechanics, 7, 3, p. 368-404. http://dx.doi.org/10.1007/s00021-004-0121-y

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Type
Article accepté pour publication ou publié
Date
2005
Journal name
Journal of Mathematical Fluid Mechanics
Volume
7
Number
3
Publisher
Springer
Pages
368-404
Publication identifier
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Author(s)
Chambolle, Antonin cc
Desjardins, Benoît
Esteban, Maria J. cc
Grandmont, Céline
Abstract (EN)
The purpose of this work is to study the existence of solutions for an unsteady fluid-structure interaction problem. We consider a three-dimensional viscous incompressible fluid governed by the Navier–Stokes equations, interacting with a flexible elastic plate located on one part of the fluid boundary. The fluid domain evolves according to the structure’s displacement, itself resulting from the fluid force. We prove the existence of at least one weak solution as long as the structure does not touch the fixed part of the fluid boundary. The same result holds also for a two-dimensional fluid interacting with a one-dimensional membrane.
Subjects / Keywords
Fluid-structure interaction; Navier–Stokes equations; Plates equations; weak solutions