Correctness of the Cauchy problem for the two-fluid model of a gas-particle mixture

The correctness of the Cauchy problem is examined in the framework of the two-fluid model for the one-dimensional unsteady flow of a mixture of gas and dispersed solid particles. The analysis is carried out both with and without allowance for the volume occupied by the particles. In both cases norms are proposed in which the problem is correct even in the case when 'small ripples' on the initial data cause intersections of particle trajectories. Particular attention is given to the introduction of norms in which the problem, incorrect in some other norm, becomes correct without changing the model.