Weak and strong solutions for a fluid-poroelastic-structure interaction via a semigroup approach

Abstract

A filtration system comprising a Biot poroelastic solid coupled to an incompressible Stokes free-flow is considered in 3D. Across the flat 2D interface, the Beavers-Joseph-Saffman coupling conditions are taken. In the inertial, linear, and non-degenerate case, the hyperbolic-parabolic coupled problem is posed through a dynamics operator on a chosen energy space, adapted from Stokes-Lamé coupled dynamics. A semigroup approach is utilized to circumvent issues associated to mismatched trace regularities at the interface. The generation of a strongly continuous semigroup for the dynamics operator is obtained via a non-standard maximality argument. The latter employs a mixed-variational formulation in order to invoke the Babuška-Brezzi theorem. The Lumer-Philips theorem then yields semigroup generation, and thereby, strong and generalized solutions are obtained. For the linear dynamics, density obtains the existence of weak solutions; we extend to the case where the Biot compressibility of constituents degenerates. Thus, for the inertial linear Biot-Stokes filtration system, we provide a clear elucidation of strong solutions and a construction of weak solutions, as well as their regularity through associated estimates.