Riemann problem for the pressureless Cargo–LeRoux model by flux perturbation

Abstract

By introducing a potential, a new formulation model of conservation laws was derived by Cargo and LeRoux from the Euler equations with a constant gravity (Cargo and LeRoux in C R Acad Sci Paris Serie I Math 318:73–76, 1994). It gives a conservative form extension of the Euler equations without external forces. This paper is concerned with the pressureless flow of the Cargo–LeRoux model. By using a flux perturbation, the solutions with three kinds of structures of the Riemann problem are constructed. The new type of structure simultaneously including delta-shock and vacuum state appears in solution. The Riemann solutions also give an interesting extension of those to the pressureless Euler equations without external forces.