Global Existence and Asymptotic Behavior of Strong Solutions to the 3D Viscous Liquid–Gas Two‐Phase Flow Model With Slip Boundary Condition

ABSTRACT This paper addresses the existence and large‐time asymptotic behavior of strong solutions to the viscous liquid–gas two‐phase flow model subject to slip boundary conditions in a three‐dimensional, simply connected bounded domain with a smooth boundary consisting of finite number 2D connected components. Compared to the Cauchy problem studied in Yu [ Journal of Differential Equations 272 (2021): 732–759] and Guo et al. [ Journal of Mathematical Physics 52 (2011): 9], the main advancement lies in overcoming key difficulties involving boundary integral estimates. We establish the global existence and uniqueness of strong solutions for the system provided that the initial energy is sufficiently small. Moreover, we characterize the large‐time decay of these solutions. Notably, our analysis allows for initial densities exhibiting large oscillations and including vacuum states.