Pressureless Magnetohydrodynamics System: Riemann Problem and Vanishing Magnetic Field Limit

Author:

Li Shiwei1ORCID,Cheng Hongjun1ORCID,Yang Hanchun1

Affiliation:

1. Department of Mathematics, Yunnan University, Kunming, Yunnan 650091, China

Abstract

This paper proposes the pressureless magnetohydrodynamics (MHD) system by neglecting the effect of pressure difference in the MHD system. Firstly, the Riemann problem for the pressureless MHD system is solved with five kinds of structures of solutions consisting of combinations of shock, rarefaction wave, contact discontinuity, and vacuum state. Secondly, the limit behavior of the obtained Riemann solutions as the magnetic field drops to zero is studied. It is shown that, as the magnetic field vanishes, the Riemann solutions of the pressureless MHD system just tend to the corresponding Riemann solutions of the Euler equations for pressureless fluids. The formation processes of delta shocks and vacuum states are clarified. For the delta shock, both the intermediate density and internal energy simultaneously develop delta measures.

Funder

National Natural Science Foundation of China

Publisher

Hindawi Limited

Subject

Applied Mathematics,General Physics and Astronomy

Cited by 2 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. FORMATION OF DELTA-SHOCKS FOR THE CHAPLYGIN GAS EQUATIONS BY LOGARITHMIC PRESSURE PERTURBATION;Rocky Mountain Journal of Mathematics;2023-08-01

2. Delta shock wave as limits of vanishing viscosity for zero‐pressure gas dynamics with energy conservation law;ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik;2022-12-16

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