Yongjin Lu, University of Virginia


Uniform stability of a nonlinear fluid structure interaction with boundary dissipation at the interface

Abstract: We consider a model of nonlinear fluid-structure interaction in a bounded two dimensional domain, where it is comprised of two open adjacent sub-domains occupied, respectively, by the solid and the fluid. This leads to a study of Navier Stokes equation coupled on the boundary with the dynamic system of elasticity. The goal of the work is to study the uniform stability of the interactive structure. It will be shown that if a boundary feedback control is inserted on the interface of the fluid and the elastic body, the energy of the system decays at a uniform rate of 1/t. If an extra damping is added on the elasticity equation, then it eliminates zero eigenvalue from the linear system and the energy decays uniformly at an exponential rate.

Advisor: Dr. Irena Lasiecka (University of Virginia)