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

TL;DR

This paper proves the global existence and analyzes the long-term behavior of strong solutions for a coupled two-phase fluid model involving Euler and Navier-Stokes equations in a bounded domain.

Contribution

It extends local existence results to global solutions and employs Lyapunov functionals to study their large-time dynamics.

Findings

Global existence of strong solutions established.

Large-time decay estimates derived.

Model derived from kinetic-fluid dynamics with particle-fluid interactions.

Abstract

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 [13[ 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 [13] 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.