论文标题
在完全浸入粘性不可压缩的流体中的弹性体模型上
On a model of an elastic body fully immersed in a viscous incompressible fluid with small data
论文作者
论文摘要
我们考虑了浸入两层不可压缩的粘性流体之间的弹性体模型。弹性位移$ w $由阻尼波方程$ w_ {tt} +αw_t +ΔW= 0 $没有任何稳定项，其中$α> 0 $，而流体由Navier-Stokes方程建模。我们假设位移的连续性以及移动界面上的应力和外部流体边界上的均匀的dirichlet边界条件。我们建立了一个〜先验估计，该估计为小初始数据提供了最终状态的全球及时良好性和指数衰减。我们证明，最终状态必须是微不足道的，除了可能在水平方向上弹性结构的小位移。
We consider a model of an elastic body immersed between two layers of incompressible viscous fluid. The elastic displacement $w$ is governed by the damped wave equation $w_{tt} + αw_t + Δw =0$ without any stabilization terms, where $α>0$, and the fluid is modeled by the Navier-Stokes equations. We assume continuity of the displacement and the stresses across the moving interfaces and homogeneous Dirichlet boundary conditions on the outer fluid boundaries. We establish a~priori estimates that provide the global-in-time well-posedness and exponential decay to a final state of the system for small initial data. We prove that the final state must be trivial, except for a possible small displacement of the elastic structure in the horizontal direction.
