The Vlasov–Maxwell–Fokker–Planck system near Maxwellians in ℝ³

ABSTRACT

Motivated by Duan and Strain [Optimal large-time behavior of the Vlasov–Maxwell–Boltzmann system in the whole space. Comm Pure Appl Math. 2011;64:1497–1546], we prove the global existence of solutions to the Vlasov–Maxwell–Fokker–Planck system near Maxwellians in the whole space by utilizing the refined energy method. In the proof of the global existence, the a priori estimates on the macroscopic component and the electromagnetic field are obtained by use of the macroscopic balance laws and the Maxwell equations, respectively. Moreover, the optimal time decay of solutions to the global Maxwellians, which can be obtained by employing the Fourier analysis.

KEYWORDS:

• Vlasov–Maxwell–Fokker–Planck system
• macro–micro decomposition
• energy method
• global existence
• optimal time decay
• Fourier analysis

AMS SUBJECT CLASSIFICATION (2010):

• 35Q84
• 82C40

Acknowledgments

The author would like to thank Professor zhenglu Jiang for helpful discussions.

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Xiaolong Wang  http://orcid.org/0000-0002-7229-4074

Correction Statement

This article has been republished with minor changes. These changes do not impact the academic content of the article.

Additional information

Funding

This work was supported by Doctoral Start-up Foundation of ECUT(DHBK2018055) and National Natural Science Foundation of China (Grant No.41962019).