On global solutions to a viscous compressible two-fluid model with unconstrained transition to single-phase flow in three dimensions

TL;DR

This paper proves the global existence of weak solutions for a three-dimensional viscous compressible two-fluid model with large initial data, allowing for unconstrained transition to single-phase flow and handling complex pressure interactions.

Contribution

It establishes the first global weak solution existence result for a two-fluid model with independent adiabatic constants and without initial density restrictions, accommodating phase transitions.

Findings

Global weak solutions exist for large initial data

No restrictions on initial densities or phase transitions

Applicable to models with unequal velocities and limiting systems

Abstract

We consider the Dirichlet problem for a compressible two-fluid model in three dimensions, and obtain the global existence of weak solution with large initial data and independent adiabatic constants \Gamma,\gamma>=9/5. The pressure functions are of two components solving the continuity equations. Two typical cases for the pressure are considered, which are motivated by the compressible two-fluid model with possibly unequal velocities [3] and by a limiting system from the Vlasov-Fokker-Planck/compressible Navier-Stokes system [27] (see also some other relevant models like compressible MHD system for two-dimensional case [24] and compressible Oldroyd-B model with stress diffusion [1]). The lack of enough regularity for the two densities turns out some essential difficulties in the two-component pressure compared with the single-phase model, i.e., compressible Navier-Stokes equations. In this paper, the global existence theory does not require any domination conditions for the initial densities, which implies that transition to each single-phase flow is allowed.