Singular limit of the nonisentropic compressible ideal MHD equations in a domain with boundary

ABSTRACT

In this paper, we study the singular limit of three-dimensional nonisentropic compressible ideal MHD equations with horizontal boundary conditions. It is rigorously justified that, when the Mach number and Alfvén number are same and tend to zero, the solution of original equations converges to that of two-dimensional incompressible flow.

Keywords:

• Nonisentropic compressible ideal MHD equations
• Mach number
• Alfvén number
• singular limit
• domain with horizontal boundaries

2000 Mathematics Subject Classifications:

• 76W05
• 35B40

Acknowledgments

The author would like to thank Professors Fucai Li and Qiangchang Ju for their fruitful discussions and encouragement during the preparation of this paper. This work is supported by NSFC (Grant No. 11671193).

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work is supported by NSFC [grant number 11671193].