Global strong solutions for 3-D immiscible and slightly compressible two-phase flow in porous media

In this paper, we consider the flow of two-phase slightly compressible and immiscible fluids in porous media. We focus on the case where the densities of phases follow exponential laws with small compressibility factors, the absolute permeability is linked to the porosity via a Kozeny-Carman relation, and source terms account for realistic injection and production rates. Under some realistic hypotheses based on the data, we establish the local existence and uniqueness of strong solutions for the regularized three-dimensional system. We further show that the solution is global under small assumptions for the system without source terms. This is the first high-dimensional result of the strong solution without any symmetric assumptions for immiscible two-phase flow systems in porous media.