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

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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 L2 − L∞ estimates.

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Authors and Affiliations

  1. Department of Mathematics, College of Science, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, China

    Xiuhui Yang

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  1. Xiuhui Yang
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Correspondence to Xiuhui Yang.

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

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Yang, X. Stability of the Equilibrium to the Boltzmann Equation with Large Potential Force. Chin. Ann. Math. Ser. B 39, 805–816 (2018). https://doi.org/10.1007/s11401-018-0097-1

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  • DOI: https://doi.org/10.1007/s11401-018-0097-1

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