Global existence and large time behavior of solutions for full compressible Hall-MHD equations

ABSTRACT

In this paper, we first provide a derivation of compressible nonisentropic Hall-magnetohydrodynamic (Hall-MHD) system from generalized Ohm's law. Then, we prove the global existence of strong solutions for the compressible nonisentropic Hall-MHD model based on the standard energy method in $H^2$-framework. Finally, optimal decay rates of strong solutions in $L^2$-norm are obtained if the initial data belong to $L^1$ additionally.

KEYWORDS:

• Compressible Hall-MHD equations
• global solutions
• decay rate

2010 MATHEMATICS SUBJECT CLASSIFICATIONS:

• 35A01
• 35Q35
• 35D35
• 76W05

Acknowledgments

The author would like to thank Professor Yachun Li and Professor Qilong Gu for their helpful discussion.

Disclosure statement

No potential conflict of interest was reported by the author.

Additional information

Funding

The research of Zhaoyang Shang was supported in part by National Natural Science Foundation of China [grant numbers 11571232 and 11831011].