当界面与边界相交时流固耦合的加权\(H^2\)正则性
Weighted $H^2$ regularity of fluid-structure interaction when the interface intersects the boundary
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中文总结 AI 辅助
研究二维多边形区域中流固耦合问题解的正则性，因域角几何奇异性致解正则性受限。引入加权索伯列夫空间及解算子框架，将耦合系统解耦，证明了加权索伯列夫空间\(\mathbf{H}^{2,2}_{\boldsymbol{\beta}}\)中解的存在唯一性。
中文摘要 AI 辅助
本文分析了二维多边形区域中涉及斯托克斯流体和线性弹性固体的流固耦合（FSI）问题的解的正则性。该区域由与域边界相交的界面分隔。主要挑战源于域角处几何奇异性导致的解的正则性有限。为此，引入了定制的加权索伯列夫空间\(\mathbf{H}^{k,l}_{\boldsymbol{\beta}}\)以及这些空间上的新型解算子框架。此框架为在正则性分析中将耦合的FSI系统解耦为易处理的流体和弹性固体子问题提供了关键见解。作为主要结果，证明了加权索伯列夫空间\(\mathbf{H}^{2,2}_{\boldsymbol{\beta}}\)中解的存在唯一性。
英文摘要
This paper analyzes the regularity of solutions to a fluid-structure interaction (FSI) problem involving a Stokesian fluid and a linear elastic solid in a two-dimensional polygonal domain, seperated by an interface which intersects the boundary of the domain. The main challenges arise from the limited solution regularity caused by geometric singularities at the domain corners. To address this, we introduce tailored weighted Sobolev spaces, denoted by $\mathbf{H}^{k,l}_{\boldsymbolβ}$, and a novel solution operator framework on these spaces. This framework provides the key insight for decoupling the coupled FSI system into tractable fluid and elastic solid subproblems in the regularity analysis. As our main result, we prove the existence and uniqueness of a solution in the weighted Sobolev space $\mathbf{H}^{2,2}_{\boldsymbolβ}$.
