Author(s)

Hongxia Ji, Wenjing Song

School of Science, Xi’an Polytechnic University, Xi’an, China.

In the paper, we study a compressible two-fluid model in ${ℝ}^3$ , 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 $Z=P-\overline{P}$ , 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.

Two-Fluid Model, Degenerate Viscosities, Large-Time Behavior, Global Well-Posedness

Ji, H. and Song, W. (2025) Global Well-Posedness and Large-Time Behavior to the 3D Two-Fluid Model with Degenerate Viscosities. Journal of Applied Mathematics and Physics, 13, 230-255. doi: 10.4236/jamp.2025.131010.