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Viscosity analysis on the Boltzmann equation

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Abstract

This paper is devoted to investigating the asymptotic properties of the renormalized solution to the viscosity equation ∂ t f ɛ + υ·▿ x f ɛ = Q(f ɛ ,f ɛ + ɛΔ υ f ɛ as ɛ → 0+ We deduce that the renormalized solution of the viscosity equation approaches to the one of the Boltzmann equation inL 1((0,T) × ℝN × ℝN). The proof is based on compactness analysis and velocity averaging theory.

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Authors and Affiliations

  1. School of Science, Huzhou Teachers College, Huzhou, 313000, P. R. China

    Min Ling Zheng

  2. School of Science, Nanjing University of Science & Technology, Nanjing, 210094, P. R. China

    Xiao Ping Yang

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  1. Min Ling Zheng
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  2. Xiao Ping Yang
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Correspondence to Min Ling Zheng.

Additional information

Supported by the Innovation Team Foundation of the Department of Education of Zhejiang Province (Grant No. T200924), and National Natural Science Foundation of China (Grant No. 11101140); the second author is supported by National Natural Science Foundation of China (Grant No. 11071119)

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Zheng, M.L., Yang, X.P. Viscosity analysis on the Boltzmann equation. Acta. Math. Sin.-English Ser. 28, 2139–2152 (2012). https://doi.org/10.1007/s10114-012-9582-8

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  • DOI: https://doi.org/10.1007/s10114-012-9582-8

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