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Title: Fluid-poroviscoelastic structure interaction problem with nonlinear coupling
We prove the existence of a weak solution to a fluid-structure interaction (FSI) problem between the flow of an incompressible, viscous fluid modeled by the Navier-Stokes equations, and a poroviscoelastic medium modeled by the Biot equations. The two are nonlinearly coupled over an interface with mass and elastic energy, modeled by a reticular plate equation, which is transparent to fluid flow. The existence proof is constructive, consisting of two steps. First, the existence of a weak solution to a regularized problem is shown. Next, a weak-classical consistency result is obtained, showing that the weak solution to the regularized problem converges, as the regularization parameter approaches zero, to a classical solution to the original problem, when such a classical solution exists. While the assumptions in the first step only require the Biot medium to be poroelastic, the second step requires additional regularity, namely, that the Biot medium is poroviscoelastic. This is the first weak solution existence result for an FSI problem with nonlinear coupling involving a Biot model for poro(visco)elastic media.  more » « less
Award ID(s):
2247000
NSF-PAR ID:
10502619
Author(s) / Creator(s):
Publisher / Repository:
arXiv:2307.16158
Date Published:
Journal Name:
Jorunal de Mathematiques Pures and Appliques
ISSN:
Not yet availabe
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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