On weak solutions to the compressible inviscid two-fluid model

Abstract

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.