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L2-Stability Theory of the Boltzmann Equation near a Global Maxwellian

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Abstract

We present three a priori L 2-stability estimates for classical solutions to the Boltzmann equation with a cut-off inverse power law potential, when initial datum is a perturbation of a global Maxwellian. We show that L 2-stability estimates of classical solutions depend on Strichartz type estimates of perturbations and the non-positive definiteness of the linearized collision operator. Several well known classical solutions to the Boltzmann equation fit our L 2-stability framework.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Seoul National University, Seoul, 151-747, Korea

    Seung-Yeal Ha & Seok-Bae Yun

  2. Department of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai, 200240, People’s Republic of China

    Xionfeng Yang

Authors
  1. Seung-Yeal Ha
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  2. Xionfeng Yang
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  3. Seok-Bae Yun
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Correspondence to Seung-Yeal Ha.

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Communicated by C. M. Dafermos

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Ha, SY., Yang, X. & Yun, SB. L2-Stability Theory of the Boltzmann Equation near a Global Maxwellian. Arch Rational Mech Anal 197, 657–688 (2010). https://doi.org/10.1007/s00205-010-0326-6

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  • DOI: https://doi.org/10.1007/s00205-010-0326-6

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