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author:

Shao, Z. (Shao, Z..) [1]

Indexed by:

Scopus

Abstract:

We investigate the vanishing magnetic field limits of Riemann solutions to the isentropic Chaplygin gas magnetogasdynamics equations. It is rigorously proved that, as the magnetic field vanishes, the Riemann solutions to the isentropic Chaplygin gas magnetogasdynamics equations converge to the Riemann solutions to the Chaplygin gas equations with the same initial data. Besides, substantially different from the previous works on the vanishing pressure limits of Riemann solutions, where any Riemann solution containing two shock waves converges to a delta shock solution to the transport equations and the intermediate density between the two shocks converges to a weighted δ-measure which forms the delta shock, we rigorously justify that as the magnetic field vanishes, some Riemann solutions containing two shocks tend to a delta shock solution to the Chaplygin gas equations, and the intermediate density between the two shocks tends to a weighted δ-measure which forms the delta shock; while the rest Riemann solutions containing two shock waves tend to a two-contact-discontinuity solution to the Chaplygin gas equations, the intermediate state between the two contact discontinuities is a nonvacuum state. © 2022, The Author(s), under exclusive licence to Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia.

Keyword:

Chaplygin gas equations Delta shock Isentropic Chaplygin gas magnetogasdynamics equations Rarefaction wave Riemann solutions Shock wave Vanishing magnetic field limits

Community:

  • [ 1 ] [Shao Z.]School of Mathematics and Statistics, Fuzhou University, Fuzhou, 350108, China

Reprint 's Address:

  • [Shao, Z.]School of Mathematics and Statistics, China

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Source :

Bulletin of the Malaysian Mathematical Sciences Society

ISSN: 0126-6705

Year: 2022

Issue: 6

Volume: 45

Page: 3101-3129

1 . 2

JCR@2022

1 . 0 0 0

JCR@2023

ESI HC Threshold:24

JCR Journal Grade:2

CAS Journal Grade:3

Cited Count:

WoS CC Cited Count:

SCOPUS Cited Count: 2

ESI Highly Cited Papers on the List: 0 Unfold All

WanFang Cited Count:

Chinese Cited Count:

30 Days PV: 0

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