可压缩随机流-结构相互作用：输运噪声与Navier滑移的随机流方法

中文摘要 AI 辅助

本文建立了三维随机流-结构相互作用（FSI）问题的局部鞅解的存在性，该问题通过Navier滑移边界条件将粘性可压缩等熵流体与弹性壳耦合。流体和壳受到相容的Stratonovich输运噪声的扰动。随机流变换去除了随机输运积分，并产生了一个逐路径的随机FSI系统，其拉回系数在时间上仅具有Hölder连续性。我们将多层逼近方案与有界流事件上的局部化以及短确定性时间子区间上随机系数的冻结相结合。壳输运场不需要生成等距变换：弯曲能鞅和Itô修正通过交换子恒等式在自然的$H^2$水平上得到控制，而不会损失导数。紧性在Jakubowski空间中获得，压力紧性通过局部化有效粘性通量证明，最终的人工压力和惩罚极限使用边界压力紧性和$H^2$图迹工具。对于$\u03b3>3/2$和非碰撞初始数据，我们获得了一个直到几乎必然为正的停止时间的鞅解。

英文摘要

This paper establishes the existence of local martingale solutions for a three-dimensional stochastic fluid--structure interaction (FSI) problem coupling a viscous compressible isentropic fluid with an elastic shell through Navier-slip boundary conditions. The fluid and shell are perturbed by compatible Stratonovich transport noise. A stochastic-flow transformation removes the stochastic transport integrals and produces a pathwise random FSI system whose pullback coefficients are only Hölder continuous in time. We combine a multi-layer approximation scheme with localization on bounded-flow events and freezing of the random coefficients on short deterministic time subintervals. The shell transport fields are not required to generate isometries: the bending-energy martingale and Itô correction are controlled at the natural $H^2$ level by commutator identities without derivative loss. Tightness is obtained in Jakubowski spaces, pressure compactness is proved through localized effective viscous flux, and the final artificial-pressure and penalty limit uses boundary-pressure tightness and $H^2$-graph trace tools. For $γ>3/2$ and non-colliding initial data, we obtain a martingale solution up to an almost surely positive stopping time.

发表机构

• Zhejiang Sci-Tech University（浙江理工大学）
• Southeast University（东南大学）

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