Preprint 2015-007
Delta shocks and vacuum states for the isentropic magnetogasdynamics equations for Chaplygin gas as pressure and magnetic field vanish
Zhiqiang Shao
Abstract: This paper is concerned with the Riemann problem for the isentropic Chaplygin gas magnetogas-dynamics equations and the formation of delta shocks and vacuum states as pressure and magnetic field vanish. Firstly, the Riemann problem of the isentropic magnetogasdynamics equations for Chaplygin gas is solved analytically. Secondly, it is rigorously proved that, as both the pressure and the magnetic field vanish, the Riemann solution containing two shock waves tends to a delta shock solution to the transport equations, and the intermediate density between the two shocks tends to a weighted δ-measure which forms the delta shock; while the Riemann solution containing two rarefaction waves tends to a two-contact-discontinuity solution to the transport equations, the intermediate state between the two contact discontinuities is a vacuum state.