Mathematical theory of stationary miscible filtration

AbstractWe consider a coupled system of two elliptic partial differential equations that models stationary incompressible two-component miscible displacement in porous media. We suppose that the dispersion tensor depends on the velocity (the so-called Peaceman model, see, e.g., [D. W. Peaceman, Soc. Pet. Eng. J. 6 (1966), 213–216]. Assuming that the mobility ratio is not too large, we prove the existence of at least one solution in Wr2(Ω) × Wr2(Ω). Furthermore, supposing that the data are small, we also establish well-posedness in Wr2(Ω) × Wl1(Ω)