发表机构
University of Duisburg-Essen; African Institute for Mathematical Sciences（杜伊斯堡-埃森大学; 非洲数学科学研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对二维流固耦合中弹性壳长期自相交的开放问题，本文通过在结构方程中加入足够强的输运噪声，证明在任意给定时间前自相交不会以任意小于1的概率发生。
AI 中文摘要
我们考虑二维空间中粘性不可压缩流体与占据流体域边界的柔性弹性壳之间的相互作用。该壳由完全弹性的线性化梁方程建模。在流固耦合中，即使对于完全弹性板的理想化情形，长期内能否排除结构的自相交仍是一个开放问题。我们证明，通过在结构方程中添加一个物理上动机充分且足够强的输运噪声，在任意给定的终止时间之前，自相交不会以任意小于1的规定概率发生。
英文摘要
We consider the interaction of a viscous incompressible fluid with a flexible elastic shell occupying the boundary of the fluid's domain in two space dimensions. The shell is modelled by a perfectly elastic linearised beam equation. It is an open problem in fluid-structure interaction, even for the idealised case of a perfectly elastic plate, if a self-intersection of the structure can be excluded in the long run. We show that by adding a physically well-motived and sufficiently strong transport noise in the structure equation, the self-intersection does not occur before any given end-time with any prescribed probability smaller than 1.
