带对数气体的等熵磁气动力学在体力作用下黎曼解的极限研究

数学物理学报 ›› 2025, Vol. 45 ›› Issue (5): 1477-1491.

带对数气体的等熵磁气动力学在体力作用下黎曼解的极限研究

王伟斌(),邵志强^*()

福州大学数学与统计学院福州 350108

收稿日期:2023-12-14 修回日期:2025-03-11 出版日期:2025-10-26 发布日期:2025-10-14
通讯作者: * 邵志强,E-mail:zqshao@fzu.edu.cn
作者简介:王伟斌, E-mail:1434667875@qq.com
基金资助:
福建省自然科学基金(2019J01642)

Delta Shocks and Vacuum States in Vanishing Pressure and Magnetic Field Limits of Solutions to the Isentropic Magnetogasdynamics with the Logarithmic Equation of State Under the Body Force

Weibin Wang(),Zhiqiang Shao^*()

School of Mathematics and Statistics, Fuzhou University, Fuzhou 350108

Received:2023-12-14 Revised:2025-03-11 Online:2025-10-26 Published:2025-10-14
Supported by:
Natural Science Foundation of Fujian Province(2019J01642)

摘要/Abstract

摘要：

该文利用变换求解了体力作用下等熵磁气体动力学的黎曼问题. 该问题中的状态方程包括一个对数函数. 该文证明了当压力和磁场趋于零时, 解中存在 $\delta$- 激波和真空状态. 此外, 还严格证明, 当压力和磁场都消失时, 具有两个激波的黎曼解收敛到输运方程中的 $\delta$-激波解, 而具有两个稀疏波的黎曼解收敛到一个由四个接触不连续以及极限场景中具有三种不同虚拟速度的真空态组成的解.

关键词: 等熵磁气动力学, 黎曼问题, 黎曼解, $\delta$-激波, 真空状态

Abstract:

In this paper, we use a transformation to solve the Riemann problem for isentropic magnetogasdynamics under the body force. The equation of state in this problem includes a logarithmic function. We prove the existence of $\delta$-shocks and vacuum states in solutions when the pressure and magnetic field tend to zero. Additionally, it is rigorously proved that, when both the pressure and magnetic field vanish, a Riemann solution with two shock waves converges to a delta shock wave solution in the transport equations; while a Riemann solution with two rarefaction waves converges to a solution consisting of four contact discontinuities along with vacuum states with three different virtual velocities in the limiting scenario.

Key words: isentropic magnetogasdynamics, Riemann problem, Riemann solutions, Delta shock wave, vacuum state

中图分类号:

O175.29

王伟斌, 邵志强. 带对数气体的等熵磁气动力学在体力作用下黎曼解的极限研究[J]. 数学物理学报, 2025, 45(5): 1477-1491.

Weibin Wang, Zhiqiang Shao. Delta Shocks and Vacuum States in Vanishing Pressure and Magnetic Field Limits of Solutions to the Isentropic Magnetogasdynamics with the Logarithmic Equation of State Under the Body Force[J]. Acta mathematica scientia,Series A, 2025, 45(5): 1477-1491.

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