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| Stability of the Equilibrium to the Boltzmann Equation with Large Potential Force |
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Citation： |
Xiuhui YANG.Stability of the Equilibrium to the Boltzmann Equation with Large Potential Force[J].Chinese Annals of Mathematics B,2018,39(5):805~816 |
| Page view： 1545
Net amount： 974 |
Authors： |
Xiuhui YANG; |
Foundation： |
This work was supported by the Fundamental Research
Funds for the Central Universities (No.NS201 2122). |
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| Abstract： |
The Boltzmann equation with external potential force exists a
unique \linebreak 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 $\mathbb{R}^3$. Compared with the previous result [Ukai,
S., Yang, T. and Zhao, H.-J., Global solutions to the Boltzmann
equation with external forces, {\it Anal. Appl.} ({\it Singap}.),
\textbf{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 $L^2-L^\infty$
estimates. |
Keywords： |
Boltzmann equation, Large potential force, Stability,Entropy-energy inequality, $L^2-L^infty$ method |
Classification： |
76P05, 82C40, 35B35 |
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