Consider a model of flow of two compressible or incompressible and immiscible phases in a three dimensional porous media. The existence of a weak solution is obtained for two compressible immiscible fluids when the porosity depends on the global pressure and on the space variable.
"Two compressible immiscible fluids in porous media: the case where the porosity depends on the pressure." Adv. Differential Equations 13 (7-8) 781 - 800, 2008.