Delta shocks and vacuum states for the isentropic magnetogasdynamics equations for Chaplygin gas as pressure and magnetic field vanish

• DOI: 10.1007/s13324-022-00692-8
• Publication Date: 2022-05-31T04:02:36Z
• Authors: Zhiqiang Shao
• Keywords: Isentropic process; Classification of discontinuities; Chaplygin gas; Discontinuity (linguistics); Rarefaction (ecology)

This paper is concerned with the Riemann problem for the isentropic Chaplygin gas magnetogasdynamics 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 $��$-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 termediate state between the two contact discontinuities is a vacuum state.