A note on viscous liquid–gas two-phase flow model with mass-dependent viscosity and vacuum

In this paper, we consider a free boundary value problem for two-phase liquid–gas model with mass-dependent viscosity coefficient; the gas is assumed to be polytropic whereas the liquid is treated as an incompressible fluid, and the fluid velocities are unequal, i.e., ug≠ulug≠ul. The local existence of a weak solution is established when the initial gas mass connects to vacuum continuously.