ABSTRACT
Abstract We report on some recent progress in the mathematical theory of fluid transport and poromechanics, specifically, the exchange of fluid between the Biot model of an elastic porous structure saturated with a slightly compressible viscous fluid coupled to the Stokes flow in an adjacent open channel. The coupled system is resolved by semigroup methods by developing appropriate variational formulations. These lead to either a standard weak formulation or a mixed formulation for the resolvent equation.
