Well-posedness for the coupling between a viscous incompressible fluid and an elastic structure. (20th August 2019)

• Record Type: Journal Article
• Authors: Boulakia, Muriel; Guerrero, Sergio; Takahashi, Takéo
• Is Part Of: Nonlinearity. Volume 32:Number 10(2019)
• Page Start: 3548
• Page End: 3592
• Publication Date: 2019-08-20
• Subjects: fluid-structure -- Navier–Stokes system -- elastic structure; 76D03 -- 76D05 -- 35Q74 -- 76D27; Nonlinear theories -- Periodicals; Mathematical analysis -- Periodicals; Mathematical analysis; Nonlinear theories; Periodicals; 515
• DOI: 10.1088/1361-6544/ab128c
• Languages: English
• ISSNs: 0951-7715

Abstract

Abstract: In this paper, we consider a system modeling the interaction between a viscous incompressible fluid and an elastic structure. The fluid motion is represented by the classical Navier–Stokes equations while the elastic displacement is described by the linearized elasticity equation. The elastic structure is immersed in the fluid and the whole system is confined into a general bounded smooth domain of . Our main result is the local in time existence and uniqueness of a strong solution of the corresponding system.