Global strong solutions to the 3D viscous liquid–gas two–phase flow model

This paper concerns strong solutions to the 3D viscous liquid–gas two–phase flow model with initial vacuum. Strong solutions are proved to exist globally in time under the assumption that initial data is small in some sense. Compared to previous results, the major step forward is that the initial masses of liquid and gas are allowed to contain some vacuum regions and the higher–order estimates of the two masses and pressure are established, without any constraints between the initial masses of liquid and gas.