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We propose and analyze a model for solving the coupled problem arising in the interaction of a free fluid with a poroelastic medium. The flow in the fluid region is described by the Stokes equations and in the poroelastic medium by the quasi-static Biot model. The focus of the model is on quasi-Newtonian fluids that exhibit a shear-thinning property. We establish existence and uniqueness of the solution for two alternative formulations of the proposed model.

A nonlinear Stokes–Biot model for the interaction of a non-Newtonian fluid with poroelastic media