Small data global existence for a fluid-structure model
We address the system of partial differential equations modeling motion of an elastic body inside an incompressible fluid. The fluid is modeled by the incompressible Navier-Stokes equations while the structure is represented by the damped wave equation with interior damping. The additional boundary stabilization γ, considered in our previous paper, is no longer necessary. We prove the global existence and exponential decay of solutions for small initial data in a suitable Sobolev space.
Ignatova, M., Kukavica, I., Lasiecka, I., & Tuffaha, A. (2017). Small data global existence for a fluid-structure model. Nonlinearity, 30 (2), 848-898. https://doi.org/10.1088/1361-6544/aa4ec4