论文标题
非线性流体结构相互作用的全球存在和融合到压力波
Global existence and convergence to pressure waves in nonlinear fluid-structure interaction
论文作者
论文摘要
我们考虑一个非线性系统，对浸入不可压缩的粘性流体中的线性弹性体的动力学进行建模，而不会阻尼弹性部分。我们证明了局部存在强大的解决方案和全球存在和对小数据的独特性。同时，根据几何设置，非平凡的时间周期溶液（称为压力波）可能会持续存在。我们的主要结果是弹性位移的长时间行为的表征：最高刚性运动，要么系统静止或收敛到压力波。
We consider a non-linear system modelling the dynamics of a linearly elastic body immersed in an incompressible viscous fluid, without damping on the elastic part. We prove local existence of strong solutions and global existence and uniqueness for small data. At the same time, depending on the geometric setting, non-trivial time-periodic solutions, called pressure waves, may persist. Our main result is the characterization of long-time behaviour of the elastic displacement: up to small rigid motions, either the system comes to rest or converges to a pressure wave.
