标题： 三维Navier-Stokes-Biot耦合通过移动的网格板界面：弱解的存在性 显示英文标题

标题： Three-dimensional Navier-Stokes-Biot coupling via a moving reticular plate interface: existence of weak solutions

摘要： 我们证明了涉及不可压缩、粘性、牛顿流体和多层多孔（粘弹性）结构的正则化三维流体-结构相互作用（FSI）问题存在有限能量弱解。 该结构由一个由Biot方程建模的厚层和一个具有惯性和弹性能量、对流体流动透明的薄网状板组成。 耦合是非线性的，因为它是在一个未知的移动界面上进行的，该界面不是先验已知的，而是由解本身定义的，使得该问题成为移动边界问题。 这种非线性自由边界耦合，加上Biot位移的有限正则性，使得经典的弱公式在有限能量下定义不清。 为了解决这个问题，我们引入了一种最小侵入性正则化方法，基于Biot位移的适当扩展和卷积，选择使得正则化问题与原始模型保持一致。 然后我们通过Lie算子分裂方案构造正则化问题的近似解，并推导出统一的能量界限。 虽然这些界限保证了弱和弱*收敛，但在非线性项中取极限需要更精细的紧致性论证，包括Aubin-Lions引理的变体以及适用于移动非Lipschitz界面的工具。 该结果特别适用于纯弹性情况（无结构阻尼）以及多孔粘弹性情况。 这项工作将Kuan-Čanić-Muha 2024的二维分析扩展到完全三维设置，并据我们所知，提供了第一个对于具有渗透界面的非线性耦合、多层三维Navier-Stokes-Biot FSI系统的存在性结果。 显示英文摘要

摘要： We prove the existence of finite-energy weak solutions to a regularized three-dimensional fluid-structure interaction (FSI) problem involving an incompressible, viscous, Newtonian fluid and a multilayered poro(visco)elastic structure. The structure consists of a thick layer modeled by the Biot equations and a thin reticular plate with inertia and elastic energy, transparent to fluid flow. The coupling is nonlinear in the sense that it takes place on a moving interface that is not known a priori but is defined by the solution itself, making the problem a moving-boundary problem. This nonlinear free-boundary coupling, combined with the limited regularity of the Biot displacement, renders the classical weak formulation ill-defined at finite energy. To address this, we introduce a minimally invasive regularization based on a suitable extension and convolution of the Biot displacement, chosen so that the regularized problem remains consistent with the original model. We then construct approximate solutions to the regularized problem via a Lie operator-splitting scheme and derive uniform energy bounds. While these bounds ensure weak and weak* convergence, passing to the limit in the nonlinear terms requires refined compactness arguments, including variants of the Aubin-Lions lemma and tools adapted to moving non-Lipschitz interfaces. The result applies in particular to the purely elastic case (without structural damping) as well as the poroviscoelastic case. This work extends the two-dimensional analysis of Kuan-\v{C}ani\'c-Muha 2024 to the fully three-dimensional setting and, to our knowledge, provides the first existence result for a nonlinearly coupled, multilayer 3D Navier-Stokes-Biot FSI system with a permeable interface.