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

Affiliation of Author(s):理学院

Journal:CHINESE ANNALS OF MATHEMATICS SERIES B

Key Words:Boltzmann equation Large potential force Stability Entropy-energy inequality L-2 - L-infinity method

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 R-3. 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 H-1 of the potential is needed in our arguments. The proof is based on the entropy-energy inequality and the L-2 - L-infinity estimates.

ISSN No.:0252-9599

Translation or Not:no

Date of Publication:2018-09-01

Correspondence Author:yxh

Date of Publication:2018-09-01