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δ-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δ-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.
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 ofδ-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.
作者
王伟斌
邵志强
Wang Weibin;Shao Zhiqiang(School of Mathematics and Statistics,Fuzhou University,Fuzhou 350108)
出处
《数学物理学报(A辑)》
北大核心
2025年第5期1477-1491,共15页
Acta Mathematica Scientia
基金
福建省自然科学基金(2019J01642)。
关键词
等熵磁气动力学
黎曼问题
黎曼解
δ-激波
真空状态
isentropic magnetogasdynamics
Riemann problem
Riemann solutions
Delta shock wave
vacuum state
