Yongjin Lu, University of Virginia


Strong Stability of a Nonlinear Fluid-Structure Interaction Model

Abstract: We consider a 2D fluid-structure interaction coupling the Navier-Stokes equations with a dynamic system of elasticity. In the model, an elastic solid is fully immersed in a fluid and the interaction is realized via an interface, the boundary of the elastic body. In the previous papers ([1], [2]), the authors proved the global-in-time existence and the regularity of weak solutions of the model. The goal of this paper is to establish the strong stability of the system for initial data in the natural energy space.

Advisor: Irena Lasiecka (University of Virginia)

References:

[1] V. Barbu, Z. Grujic, I. Lasiecka, and A. Tuffaha, Existence of the energy-level wek solutions for a nonlinear fluid-structure interaction model, Contemporary Mathematics 440 (2007), 55-82.

[2] V. Barbu, Z. Grujic, I. Lasiecka, and A. Tuffaha, Smoothness of weak solutions to a nonlinear fluid-structure interaction model, Indiana University Mathematics Journal, Vol 57 No. 3 (2008) 1173-1207.