Decay and stability of solutions to the Fokker–Planck–Boltzmann equation in

Abstract

In this paper, we use the method of constructing the compensating function introduced by Kawashima and the standard energy method to study the global existence of solutions to the Fokker–Planck–Boltzmann equation in the whole space. The time decay and uniform stability of solutions to the global Maxwellian are also obtained.

Keywords:

• Fokker–Planck–Boltzmann equation
• compensating function
• energy method
• global existence
• optimal time decay
• uniform stability

AMS Subject Classifications:

• 35Q84
• 35Q20
• 5A09

Acknowledgements

The authors would like to express their gratitude to the referee for valuable comments and suggestions, and for kindly pointing out the references [17] and [22].

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by NNSFC [grant number 11171356].