On the Cauchy problems for polymer flooding with gravitation

We study two systems of conservation laws for polymer flooding in secondary oil recovery, one with gravitation force and one without. For each model, we prove global existence of weak solutions for the Cauchy problems, under rather general assumptions on the flux functions. Approximate solutions are constructed through a front tracking algorithm, and compactness is achieved through the bound on suitably defined wave strengths. As the main technical novelty, we introduce some new nonlinear functionals that yield a uniform bound on the total variation of the flux function.