  We develop and analyze a model for the interaction of a quasi-Newtonian free
fluid with a poroelastic medium. The flow in the fluid region is described by
the nonlinear Stokes equations and in the poroelastic medium by the nonlinear
quasi-static Biot model. Equilibrium and kinematic conditions are imposed on
the interface. We establish existence and uniqueness of a solution to the weak
formulation and its semidiscrete continuous-in-time finite element
approximation. We present error analysis, complemented by numerical
experiments.
