# Global weak solution to the viscous two-fluid model with finite energy

## TL;DR

This paper proves the existence of global weak solutions for the three-dimensional compressible two-fluid Navier-Stokes equations with large initial data, addressing the challenge of variable pressure dependence.

## Contribution

It introduces a variable reduction method for the pressure law, enabling strong convergence of densities and establishing global solutions for large data.

## Key findings

- Existence of global weak solutions in 3D for large data
- Strong convergence of densities achieved
- New variable reduction technique for pressure law

## Abstract

In this paper, we prove the existence of global weak solutions to the compressible two-fluid Navier-Stokes equations in three dimensional space. The pressure depends on two different variables from the continuity equations. We develop an argument of variable reduction for the pressure law. This yields to the strong convergence of the densities, and provides the existence of global solutions in time, for the compressible two-fluid Navier-Stokes equations, with large data in three dimensional space.