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

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
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Authors:

Xiuhui YANG;

Foundation:

This work was supported by the Fundamental Research Funds for the Central Universities (No.NS201 2122).
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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