2024/01/08 by Avalos, George, Gurvich, Elena, Webster, Justin T. · 4 citations
#35D30 #35M13 #74F10 #76M30 #76S05 #Analysis of PDEs (math.AP) #FOS: Mathematics
paper · doi:10.48550/arxiv.2401.03897
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 an appropriate energy space, adapted from Stokes-Lamé coupled dynamics. A semigroup approach is utilized to circumvent issues associated to mismatched trace regularities at the interface. C0-semigroup generation for the dynamics operator is obtained with a non-standard maximality argument. The latter employs a mixed-variational formulation in order to invoke the Babuška-Brezzi theorem. The Lumer-Philips theorem yields semigroup generation, and thereby, strong and generalized solutions are obtained. As the dynamics are linear, a standard argument by density obtains weak solutions; we extend this argument to the case where the Biot compressibility of constituents degenerates. Thus, for the inertial Biot-Stokes filtration, we provide a clear elucidation of strong and weak solutions, as well as their regularity through associated estimates.