Naslov
Multilayered Poroelasticity Interacting with Stokes Flow

Autori
Bociu, Lorena ; Canic, Sunčica ; Muha, Boris ; Webster, Justin T.

Izvornik
Siam journal on mathematical analysis (0036-1410) 53 (2021), 6; 6243-6279

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
poroelasticity ; fluid-poroelastic structure interaction ; poroelastic plate ; multilayered poroelasticity ; well-posedness

Sažetak
We consider the interaction between an incompressible, viscous fluid modeled by the dynamic Stokes equation and a multilayered poroelastic structure which consists of a thin, linear, poroelastic plate layer (in direct contact with the free Stokes flow) and a thick Biot layer. The fluid flow and the elastodynamics of the multilayered poroelastic structure are fully coupled across a fixedint erface through physical coupling conditions (including the Beavers–Joseph– Saffman condition), which present mathematical challenges related to the regularity of associated velocity traces. We prove the existence of weak solutions to this fluid-structure interaction problem with either (i) a linear, dynamic Biot model or (ii) a nonlinear quasi-static Biot component, where the permeability is a nonlinear function of the fluid content (as motivated by biological applications). The proof is based on constructing approximate solutions through Rothe’s method and using energy methods and a version of the Aubin–Lions compactness lemma (in the nonlinear case) to recover the weak solution as the limit of approximate subsequences. We also provide uniqueness criteria and show that constructed weak solutions are indeed strong solutions to the coupled problem if one assumes additional regularity.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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