Weak Solutions and Inertial Limits for Quasi-static Filtrations
Abstract
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. These dynamics cannot be easily recovered by simply sending the inertial parameters to zero; however, inserting a viscoelastic regularization of the inertial Biot system allows us to construct weak solutions in the inertial limit. Subsequently, we can pass to the limit in the regularization parameter to obtain quasi-static weak solutions. This addresses an open singular/degenerate limiting problem in the class of filtration models, and permits future analyses of uniqueness and regularity of solutions. This linear construction also provides a foundation for the later incorporation of physically-motivated nonlinear poroelastic effects via fixed point methods.
Related
- Quasi-projective dimension for complexes via filtrations
- Quasi-Static Fault-Tolerant Feedback Control of a Quadrotor under Rotor Failure with Provable Safety Guarantees
- A locking-free virtual element method for the three-dimensional quasi-static electroporoelasticity equations
- Exact non-static cylindrical solutions of Einstein’s field equations with imperfect fluids
- Serrin-type overdetermination in scaling limits: Sharp existence and asymptotic behavior of quasi-linear Schrödinger energy ground states
BibTeX
@misc{lavagnino2026weak,
title = {{Weak Solutions and Inertial Limits for Quasi-static Filtrations}},
author = {Peter Lavagnino and Arum Lee and Justin T. Webster},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2605.15007},
eprint = {2605.15007},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.15007},
}
RIS
TY - UNPB
TI - Weak Solutions and Inertial Limits for Quasi-static Filtrations
AU - Peter Lavagnino
AU - Arum Lee
AU - Justin T. Webster
PY - 2026
DA - 2026/08/28
PB - arXiv
DO - 10.48550/arxiv.2605.15007
UR - https://arxiv.org/abs/2605.15007
AB - 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. These dynamics cannot be easily recovered by simply sending the inertial parameters to zero; however, inserting a viscoelastic regularization of the inertial Biot system allows us to construct weak solutions in the inertial limit. Subsequently, we can pass to the limit in the regularization parameter to obtain quasi-static weak solutions. This addresses an open singular/degenerate limiting problem in the class of filtration models, and permits future analyses of uniqueness and regularity of solutions. This linear construction also provides a foundation for the later incorporation of physically-motivated nonlinear poroelastic effects via fixed point methods.
ER -