Energy decay and global solutions for a damped free boundary fluid–elastic structure interface model with variable coefficients in elasticity

ABSTRACT

We study a free boundary fluid-structure interaction model. In the model, a viscous incompressible fluid interacts with an elastic body via the common boundary. The motion of the fluid is governed by Navier–Stokes equations while the displacement of the elastic structure is described by variable coefficient wave equations. The dissipation is placed on the common boundary between the fluid and the elastic body. Given small initial data, the global existence of the solutions of this system is proved and the exponential decay of solutions is obtained.

KEYWORDS:

• Fluid-structure interaction
• variable coefficient wave equations
• geometric multiplier method
• boundary dissipation
• Navier–Stokes equations
• energy decay

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• 49k20

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work is supported by the National Science Foundation of China [grants numbers 61473126 and 61573342], and Key Research Program of Frontier Sciences, CAS, no. QYZDJ-SSW-SYS011.