Uniform stabilization to equilibrium of a nonlinear fluid–structure interaction model. (October 2015)

• Record Type: Journal Article
• Authors: Lu, Yongjin
• Is Part Of: Nonlinear analysis. Volume 25(2015)
• Page Start: 51
• Page End: 63
• Publication Date: 2015-10
• Subjects: Fluid–structure interaction -- Navier–Stokes equation -- Wave equation -- Boundary feedback control -- Interior feedback control -- Uniform stability; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2015.02.006
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: We consider uniform stability to a nontrivial equilibrium of a nonlinear fluid–structure interaction (FSI) defined on a two or three dimensional bounded domain. Stabilization is achieved via boundary and/or interior feedback controls implemented on both the fluid and the structure. The interior damping on the fluid combining with the viscosity effect stabilizes the dynamics of fluid. However, this dissipation propagated from the fluid alone is not sufficient to drive uniformly to equilibrium the entire coupled system. Therefore, additional interior damping on the wave component or boundary porous like damping on the interface is considered. A geometric condition on the interface is needed if only boundary damping on the wave is active. The main technical difficulty is the mismatch of regularity of hyperbolic and parabolic component of the coupled system. This is overcome by considering special multipliers constructed from Stokes solvers. The uniform stabilization result obtained in this article is global for the fully coupled FSI model.