Global Classical Solutions to the viscous two-phase flow model with slip Boundary Conditions in 3D Exterior Domains

TL;DR

This paper proves the global existence of classical solutions for a 3D viscous two-phase flow model with slip boundary conditions in exterior domains, even with large initial pressure oscillations and vacuum states.

Contribution

It establishes the first global classical solutions for this complex two-phase flow model with slip boundary conditions in 3D exterior domains.

Findings

Global classical solutions exist under small initial energy.

Pressure can have large oscillations and vacuum states.

Solutions exhibit specific large-time behavior.

Abstract

We consider the two-phase flow model with slip boundary condition in a 3D exterior domains whose boundary is smooth. We establish the global existence of classical solutions of this system provided that the initial energy is suitably small. Moreover, the pressure has large oscillations and contains vacuum states when the initial pressure allows large oscillations and a vacuum. Finally, we also obtain the large-time behavior of the classical solutions.