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January  2018, 17(1): 127-142. doi: 10.3934/cpaa.2018008

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

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

* Corresponding author

Received  January 2017 Revised  June 2017 Published  September 2017

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

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.

Citation: Jianjun Chen, Wancheng Sheng. The Riemann problem and the limit solutions as magnetic field vanishes to magnetogasdynamics for generalized Chaplygin gas. Communications on Pure & Applied Analysis, 2018, 17 (1) : 127-142. doi: 10.3934/cpaa.2018008
##### References:

show all references

##### References:
The elementary wave curves in the phase plane
The curves of elementary waves
The limiting behaviors of the curves of elementary waves
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