Existence and Nonlinear Stability of Steady-States to Outflow Problem for the Full Two-Phase Flow

TL;DR

This paper investigates the existence and nonlinear stability of steady states in a full two-phase flow model's outflow problem, revealing differences from isentropic models and providing decay rate results for various flow states.

Contribution

It establishes the existence, uniqueness, and stability of steady states for the full two-phase flow outflow problem, including subsonic, sonic, and supersonic cases, with decay rate analysis.

Findings

Steady states exist and are unique for different flow regimes.

Stability of steady states is proven for all regimes.

Decay rates are exponential for supersonic and algebraic for sonic states.

Abstract

The outflow problem for the viscous full two-phase flow model in a half line is investigated in the present paper. The existence, uniqueness and nonlinear stability of the steady-state are shown respectively corresponding to the supersonic, sonic or subsonic state at far field. This is different from the outflow problem for the isentropic Navier-Stokes equations, where there is no steady-state for the subsonic state. Furthermore, we obtain either exponential time decay rates for the supersonic state or algebraic time decay rates for supersonic and sonic states in weighted Sobolev spaces.