EXISTENCE OF SOLUTIONS TO THE RIEMANN PROBLEM FOR A MODEL OF TWO-PHASE FLOWS

We study the existence of solutions of the Riemann problem for a model of two-phase flows. The model has the form of a nonconservative hyperbolic system of balance laws. Based on a phase decomposition approach, we obtain all the wave curves. By developing an analytic method, we can establish a system of nonlinear algebraic equations for each solution of the Riemann problem. The system is under-determined and can be parameterized by the volume fraction in one phase. Therefore, an argument relying on the Implicit-Function Theorem leads us to the existence of solutions of the Riemann problem for the model for sufficiently large initial data. Furthermore, the structure of the Riemann solutions obtained by this method can also be obtained.