Weak Solutions and Inertial Limits for Quasi-static Filtrations
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| Format: | Preprint |
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2026
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| _version_ | 1866911685865897984 |
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| author | Lavagnino, Peter Lee, Arum Webster, Justin T. |
| author_facet | Lavagnino, Peter Lee, Arum Webster, Justin T. |
| contents | A quasi-static filtration system, comprising a poroelastic solid coupled to an incompressible free-flow, is considered in 3D. Across a flat 2D interface, the Beavers-Joseph-Saffman coupling conditions are taken. The system constitutes a doubly elliptic-parabolic coupling and can be seen as a degenerate case of the inertial Biot-Stokes dynamics of recent interest. These dynamics cannot be easily recovered through a vanishing inertia limit, however, utilizing a viscoelastic regularization of the inertial Biot system allows us to construct weak solutions in the inertial limit; subsequently, we pass to the limit in the regularization parameter to obtain quasi-static weak solutions. This addresses an open singular/degenerate limiting problem in filtrations, and allows for subsequent analysis of uniqueness and regularity. This also provides a foundation for the incorporation of physically-motivated nonlinear poroelastic effects. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_15007 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Weak Solutions and Inertial Limits for Quasi-static Filtrations Lavagnino, Peter Lee, Arum Webster, Justin T. Analysis of PDEs 74F10, 76S05, 35M13, 76M30, 35D30 A quasi-static filtration system, comprising a poroelastic solid coupled to an incompressible free-flow, is considered in 3D. Across a flat 2D interface, the Beavers-Joseph-Saffman coupling conditions are taken. The system constitutes a doubly elliptic-parabolic coupling and can be seen as a degenerate case of the inertial Biot-Stokes dynamics of recent interest. These dynamics cannot be easily recovered through a vanishing inertia limit, however, utilizing a viscoelastic regularization of the inertial Biot system allows us to construct weak solutions in the inertial limit; subsequently, we pass to the limit in the regularization parameter to obtain quasi-static weak solutions. This addresses an open singular/degenerate limiting problem in filtrations, and allows for subsequent analysis of uniqueness and regularity. This also provides a foundation for the incorporation of physically-motivated nonlinear poroelastic effects. |
| title | Weak Solutions and Inertial Limits for Quasi-static Filtrations |
| topic | Analysis of PDEs 74F10, 76S05, 35M13, 76M30, 35D30 |
| url | https://arxiv.org/abs/2605.15007 |