Energy decay and global solutions for a damped free boundary fluid–elastic structure interface model with variable coefficients in elasticity. Issue 11 (17th August 2020)

• Record Type: Journal Article
• Authors: Qin, Yizhao; Yao, Peng-Fei
• Is Part Of: Applicable analysis. Volume 99:Issue 11(2020)
• Page Start: 1953
• Page End: 1971
• Publication Date: 2020-08-17
• Subjects: Fluid-structure interaction -- variable coefficient wave equations -- geometric multiplier method -- boundary dissipation -- Navier–Stokes equations -- energy decay; 49k20; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2018.1551996
• Languages: English
• ISSNs: 0003-6811

Abstract

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.