The Cauchy problem for multiphase first-contact miscible models with viscous fingering

In this paper, the Cauchy problem for multiphase first-contact miscible models with viscous fingering, is studied and a global weak solution is obtained by using a new technique from the Div–Curl lemma in the compensated compactness theorem. This work extends the previous works, (Juanes and Blunt, 2006; Barkve, 1989), which provided the analytical solutions and the entropy solutions respectively, of the Riemann problem, and (Lu, 2013), which provided the global solution of the Cauchy problem for the Keyfitz–Kranzer system.