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

Abstract

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

CLC Number:

O175.29

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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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

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