Global existence and optimal convergence rates for the strong solutions in H2H2 to the 3D viscous liquid–gas two-phase flow model

This paper is concerned with the Cauchy problem of the three-dimensional viscous liquid–gas two-phase flow model. We prove the global existence of a strong solution when H2H2-norm of the initial perturbation around a constant state is sufficiently small and its L1L1-norm is bounded. Moreover, the optimal convergence rates are also obtained for such a solution.