Delta shocks and vacuum states in the Euler equations for nonisentropic magnetogasdynamics with the flux perturbation

Abstract

In this paper, we study the formation of delta shocks and vacuum states in Riemann solutions to nonisentropic magnetogasdynamics with the flux perturbation as the pressure, magnetic field and flux perturbation all vanish. First, the Riemann problem of this model is solved. Second, it is rigorously shown that, as the pressure, magnetic field and flux perturbation vanish, any Riemann solution consisting of two shocks and a possible one-contact-discontinuity to nonisentropic magnetogasdynamics with the flux perturbation tends to a delta shock solution to the transport equations, and the intermediate density between the two shocks tends to a weighted $$\delta $$-measure which forms the delta shock wave; any Riemann solution consisting of two rarefaction waves and a possible one-contact-discontinuity tends to a two-contact-discontinuity solution to the transport equations, and the nonvacuum intermediate state between the two rarefaction waves tends to a vacuum state. Finally, some numerical results are presented to verify the formation of delta shocks and vacuum states.