The Riemann problem and the limit solutions as magnetic field vanishes to magnetogasdynamics for generalized Chaplygin gas

Jianjun Chen; Wancheng Sheng

doi:10.3934/cpaa.2018008

Article Contents

2018, Volume 17, Issue 1: 127-142. Doi: 10.3934/cpaa.2018008

This issue Previous Article Multiplicity of solutions to Kirchhoff type equations with critical Sobolev exponent Next Article Nonlinear SchrÖdinger equations with sum of periodic and vanishing potentials and sign-changing nonlinearities

The Riemann problem and the limit solutions as magnetic field vanishes to magnetogasdynamics for generalized Chaplygin gas

Jianjun Chen and
Wancheng Sheng^,

Department of Mathematics, Shanghai University, Shanghai, 200444, China

* Corresponding author
* Corresponding author

Received: December 31, 2016

Revised: May 31, 2017

Published: December 2017

Supported by NSF of China (11371240) and Shanghai Municipal Education Commission of Scientific Research Innovation Project (11ZZ84).

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Abstract

This paper is concerned with the Euler equations in the magnetogasdynamics for generalized Chaplygin gas. The global solutions to the Riemann problems of the Euler equations in the magnetogasdynamics for generalized Chaplygin gas are obtained constructively by using phase plane analysis method. The formation of delta shock wave is studied as magnetic field vanishes. The limit behaviors of the Riemann solutions as magnetic field vanishes are also obtained.

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Mathematics Subject Classification: Primary:35L65, 35J70, 35R35;Secondary:35J65.

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Figure 1. The elementary wave curves in the phase plane

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Figure 2. The curves of elementary waves

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Figure 3. The limiting behaviors of the curves of elementary waves

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