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

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 H ¹ of the potential is needed in our arguments. The proof is based on the entropy-energy inequality and the L ² − L ^∞ estimates.

Keywords

Boltzmann equation / Large potential force / Stability / Entropy-energy inequality / L ² − L ^∞ method

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