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. At the end of the paper we show adaptation of our main results to other two-fluid models, and local-in-time existence and uniqueness of classical solutions.

我们考虑描述具有相同速度并享受代数压力闭合的两种流体的时间演化的可压缩无粘性模型。通过使用凸积分技术，我们证明了对于任何平滑的初始数据，存在无限多个全局时间弱解。我们还表明，对于任何分段常数初始密度，都存在合适的初始速度，使得该问题允许无限多个全局时间弱解，这些弱解的总能量守恒。在论文的最后，我们展示了我们的主要结果对其他双流体模型的适应性，以及经典解的局部时间存在性和唯一性。