Global-in-time dynamics of the two-phase fluid model in a bounded domain

In this work, we study the global existence of strong solutions and large-time behavior of a two-phase fluid model in a bounded domain. The model consists of the isothermal Euler equations and the isentropic compressible Navier–Stokes equations, coupled via the drag force. It was derived in Choi and Jung (2021) from a kinetic-fluid model describing the dynamics of particles subject to local alignment force and Brownian noises immersed in a compressible viscous fluid. For this system, we extend the local existence theory for strong solutions developed in Choi and Jung (2021) to obtain the global existence of strong solutions to the system. Moreover, we use the Lyapunov functional associated with the system to get large-time behavior estimates for global classical solutions.