Limiting behavior of scaled general Euler equations of compressible fluid flow

The aim of this article is to study the limiting behavior of the solution of Riemann problem for the scaled generalized Euler equations of compressible fluid flow. For any Riemann-type initial data, we showed the existence of solution which consists of shock waves and rarefaction waves and that the distributional limit of the solutions for this system converges to the solution of a non-strictly hyperbolic system, called one-dimensional model for large-scale structure formation of the universe as the scaling parameter vanishes. An explicit entropy and entropy flux pair is also constructed for the particular flux function (Brio system), and it is shown that the solution constructed is entropy admissible.