Well-posedness for the coupling between a viscous incompressible fluid and an elastic structure

Muriel Boulakia (1, 2, 3) , Sergio Guerrero (1, 2) , Takeo Takahashi (4, 5)

1 SU - Sorbonne Université
2 LJLL (UMR_7598) - Laboratoire Jacques-Louis Lions
3 COMMEDIA - COmputational Mathematics for bio-MEDIcal Applications
4 SPHINX - Systems with physical heterogeneities : inverse problems, numerical simulation, control and stabilization
5 IECL - Institut Élie Cartan de Lorraine

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 R3. Our main result is the local in time existence and uniqueness of a strong solution of the corresponding system.

Mots clés: Elastic structure; Fluid-structure; Navier-Stokes system

Domaines: Equations aux dérivées partielles [math.AP]

Muriel Boulakia, Sergio Guerrero, Takeo Takahashi. Well-posedness for the coupling between a viscous incompressible fluid and an elastic structure. Nonlinearity, 2019, 32, pp.3548-3592. ⟨10.1088/1361-6544/ab128c⟩. ⟨hal-01939464⟩