Global Classical Solutions of Viscous Liquid-gas Two-phase Flow Model

TL;DR

This paper proves the global existence and uniqueness of classical solutions for a 3D viscous liquid-gas two-phase flow model with small initial energy, extending methods from compressible Navier-Stokes equations.

Contribution

It establishes the first rigorous proof of global classical solutions for the viscous liquid-gas two-phase flow model under small initial energy conditions.

Findings

Global classical solutions exist and are unique.

Solutions are valid for all time with small initial energy.

Method extends continuity approach from Navier-Stokes to two-phase flow.

Abstract

In this paper, we consider the global existence and uniqueness of the classical solutions for the 3D viscous liquid-gas two-phase flow model. Initial data is only small in the energy-norm. Our main ideas come from [15] where the existence of global classical solutions to the compressible Navier-Stokes equations was obtained by using the continuity methods under the assumption that the initial energy is sufficiently small.