Three-dimensional Navier-Stokes-Biot coupling via a moving reticular plate interface: existence of weak solutions
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866913998185693184 |
|---|---|
| author | Brandt, Felix Čanić, Sunčica Muha, Boris |
| author_facet | Brandt, Felix Čanić, Sunčica Muha, Boris |
| contents | 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-Čanić-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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_14310 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Three-dimensional Navier-Stokes-Biot coupling via a moving reticular plate interface: existence of weak solutions Brandt, Felix Čanić, Sunčica Muha, Boris Analysis of PDEs 74F10, 35Q30, 35R35, 74H20 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-Čanić-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. |
| title | Three-dimensional Navier-Stokes-Biot coupling via a moving reticular plate interface: existence of weak solutions |
| topic | Analysis of PDEs 74F10, 35Q30, 35R35, 74H20 |
| url | https://arxiv.org/abs/2508.14310 |