  In three space dimensions, we consider the compressible inviscid model
describing the time evolution of two fluids sharing the same velocity and
enjoying the algebraic pressure closure. By employing the technique of convex
integration, we prove the existence of infinitely many global-in-time weak
solutions for any smooth initial data. We also show that for any piecewise
constant initial densities, there exists suitable initial velocity such that
the problem admits infinitely many global-in-time weak solutions that conserve
the total energy. The structure of the two-fluid model is crucial in our
analysis. Adaptations of the main results to other two-fluid models, like the
liquid-gas flow, are available. Local-in-time existence and uniqueness of
classical solutions will also be shown.
