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Chinese Annals of Mathematics, Series B

, Volume 39, Issue 5, pp 805–816 | Cite as

Stability of the Equilibrium to the Boltzmann Equation with Large Potential Force

  • Xiuhui Yang
Article

Abstract

The Boltzmann equation with external potential force exists a unique equilibrium—local Maxwellian. The author constructs the nonlinear stability of the equilibrium when the initial datum is a small perturbation of the local Maxwellian in the whole space ℝ3. Compared with the previous result [Ukai, S., Yang, T. and Zhao, H.-J., Global solutions to the Boltzmann equation with external forces, Anal. Appl. (Singap.), 3, 2005, 157–193], no smallness condition on the Sobolev norm H1 of the potential is needed in our arguments. The proof is based on the entropy-energy inequality and the L2L estimates.

Keywords

Boltzmann equation Large potential force Stability Entropy-energy inequality L2L method 

2000 MR Subject Classification

76P05 82C40 35B35 

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Copyright information

© Fudan University and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mathematics, College of ScienceNanjing University of Aeronautics and AstronauticsNanjingChina

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