Global strong solution to the Cauchy problem of one-dimensional compressible two-fluid model with large initial data and vacuum

This article is devoted to the Cauchy problem of a one-dimensional compressible two-fluid model with density-dependent viscosity. The pressure in this model is a function of the two fluid densities, while the viscosity depends solely on one of them. We prove the global existence and uniqueness of strong solutions for large initial data and vacuum. Our method relies upon some new mathematical techniques and the weighed Caffaralli–Kohn–Nirenberg inequality, which allows us to overcome the difficulties from the pressure function and the viscous term.