当压力和磁场为零时Chaubergin气体等熵磁气体动力学方程的Delta激波和真空态
Delta shocks and vacuum states for the isentropic magnetogasdynamics equations for Chaplygin gas as pressure and magnetic field vanish
摘要：
本文研究等熵Chaubergin气体磁气体动力学方程组的黎曼问题以及当压力和磁场消失时δ激波和真空态的形成。首先，解析求解了Chaubergin气体等熵磁气体动力学方程组的黎曼问题。其次，严格证明了当压力和磁场均为零时，包含两个激波的Riemann解趋于输运方程的δ激波解，两个激波之间的中间密度趋于形成δ激波的加权$δ$ -测度;而包含两个稀疏波的Riemann解则趋向于输运方程的两接触间断解，两个接触间断之间的中间状态是真空状态。
英文摘要：
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 $δ$-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 termediate state between the two contact discontinuities is a vacuum state.
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