Regularity of weak solutions for the relativistic Vlasov–Klein–Gordon system

Abstract

This article is devoted to the study of the relativistic Vlasov–Klein–Gordon system in space dimension three. The dynamical model describes a collisionless ensemble of classical particles coupled with a Klein–Gordon field. By combining the Fourier method and smoothing effect of low velocity particles, we prove a higher regularity of the field, which is widely used for the study of Vlasov equation.

Keywords:

• Relativistic Vlasov–Klein–Gordon system
• regularity
• Fourier method

MR Subject Classifications:

• 35Q83
• 35L60
• 82C21
• 82D10

Disclosure statement

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

Additional information

Funding

The authors would like to thank anonymous referees for their helpful comments and valuable suggestions concerning the presentation of this paper. This work is supported by the National Natural Science Foundation of China [Grant number 12001406] and Hubei Provincial Education Department Project [Grant number B2021095].