We consider a quasi-static fluid–structure interaction problem where the fluid is modeled by the Stokes equations and the structure is an active elastic material. More precisely, the displacement of the structure satisfies the equations of elasticity with an additional active stress, which models the presence of internal biological motors in the structure. Under smallness assumptions on the data, we prove the existence of a solution for this strongly coupled system.

中文翻译：

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粘性流体与主动结构之间准静态相互作用问题的存在性

我们考虑准静态流体-结构相互作用问题，其中流体由斯托克斯方程建模，并且结构是活性弹性材料。更准确地说，结构的位移满足附加弹性应力的弹性方程，从而对结构中内部生物马达的存在进行了建模。在数据的小假设下，我们证明了该强耦合系统的一种解决方案。