Existence of global strong solutions to a beam-fluid interaction system

Céline Grandmont (1, 2) , Matthieu Hillairet (3)

1 REO - Numerical simulation of biological flows
2 LJLL (UMR_7598) - Laboratoire Jacques-Louis Lions
3 IMAG - Institut Montpelliérain Alexander Grothendieck

We study an unsteady non linear fluid-structure interaction problem which is a simplified model to describe blood flow through viscoleastic arteries. We consider a Newtonian incompressible two-dimensional flow described by the Navier-Stokes equations set in an unknown domain depending on the displacement of a structure, which itself satisfies a linear viscoelastic beam equation. The fluid and the structure are fully coupled via interface conditions prescribing the continuity of the velocities at the fluid-structure interface and the action-reaction principle. We prove that strong solutions to this problem are global-in-time. We obtain in particular that contact between the viscoleastic wall and the bottom of the fluid cavity does not occur in finite time. To our knowledge, this is the first occurrence of a no-contact result, but also of existence of strong solutions globally in time, in the frame of interactions between a viscous fluid and a deformable structure.

Mots clés: Global Solution; Beam equation; Navier-Stokes Equations; Fluid-Structure interaction

Domaines: Equations aux dérivées partielles [math.AP]; Mécanique des fluides [physics.class-ph]; Mécanique des structures [physics.class-ph]

Céline Grandmont, Matthieu Hillairet. Existence of global strong solutions to a beam-fluid interaction system. Archive for Rational Mechanics and Analysis, 2016, 3, pp.1283-1333. ⟨10.1007/s00205-015-0954-y⟩. ⟨hal-01138736⟩