AI 中文总结
研究三维流体-结构相互作用问题，耦合纳维-斯托克斯方程与平方根阻尼板方程。通过高阶能量估计等方法，证明小初始数据下强解的指数衰减，为该流体-板模型相关研究提供重要理论成果。
AI 中文摘要
我们考虑一个三维流体-结构相互作用问题，它将随时间变化域中的不可压缩纳维-斯托克斯方程与一个平方根阻尼板方程耦合，该板方程位于流体的移动上边界。我们先验地证明了在合适的索伯列夫空间中对于足够小的初始数据，强解的指数衰减。证明结合了高阶能量估计、斯托克斯型正则性界和在小性假设下封闭的非线性自引导方案。
英文摘要
We consider a three-dimensional fluid-structure interaction problem coupling the incompressible Navier-Stokes equations in a time-dependent domain with a square-root damped plate equation, which is posed on the moving upper boundary of the fluid. We prove, a priori, the exponential decay of strong solutions for initial data that are sufficiently small in a suitable Sobolev space. The proof combines higher-order energy estimates, Stokes-type regularity bounds, and a nonlinear bootstrap scheme that closes under the smallness assumption.
