Global Well-Posedness and Large-Time Behavior to the 3D Two-Fluid Model with Degenerate Viscosities

In the paper, we study a compressible two-fluid model in ${？}^3$ , where ${\gamma }^{\pm }>1$ . The pressure of the two fluids is equal. Different from previous research, we consider that viscosity coefficient both $\mu$ and $\lambda$ are functions of density. The global well-posedness of the three-dimensional compressible two-phase flow model is an open problem due to its dissipative, nonlinear structure. In the paper, setting $m^{\pm }=M^{\pm }$ and $Z=P？\bar{P}$ , by exploiting the dissipation structure, we obtain energy estimates for $\left(Z\mathrm{,}w\mathrm{,}n\right)$ and its derivatives, then we obtain the time decay rates for $\left(Z\mathrm{,}w\mathrm{,}n\right)$ . So we derive global well-posedness and large time behavior to the three dimensional compressible two-fluid model.