Two-phase two-component flow in porous medium in low solubility regime

We study a system of equations governing liquid and gas flow in porous media. The gas phase is homogeneous while the liquid phase is composed of a liquid component and dissolved gas component. It is assumed that the gas component is weakly soluble in the liquid. We formulate a weak solution of the initial-boundary value problem and prove the existence theorem by passing to the limit in regularizations of the problem. Hypothesis of low solubility is given precise mathematical meaning.