Boundary stabilization of an elastic body surrounding a viscous incompressible fluid. (July 2022) - Do, K.D.
Abstract: This paper considers the problem of boundary feedback stabilization of an elastic body surrounding a viscous incompressible fluid described by Navier–Stokes equations in three dimensional space. The paper gives a proof of global existence of a weak solution of the closed-loop system via the Galerkin method. Due to consideration of less regular initial values of the fluid velocity, the forces induced by the fluid on the elastic body are not able to bound. Therefore, the paper handles "fluid work and fluid power" on the elastic body in stability and convergence analysis of the closed-loop system.