数学物理学报(英文版) ›› 2015, Vol. 35 ›› Issue (4): 887-905.doi: 10.1016/S0252-9602(15)30027-8

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ON THE ASYMPTOTIC DYNAMICS OF THE VLASOV-YUKAWA-BOLTZMANN SYSTEM NEAR VACUUM

Sun-Ho CHOI, Seung-Yeal HA   

  • 收稿日期:2015-03-09 出版日期:2015-07-01 发布日期:2015-07-01
  • 基金资助:

    The work of S.-Y. Ha is partially supported by a National Research Foundation of Korea Grant funded by the Korean Government (2014R1A2A205002096). The work of S.-H. Choi is supported by BK21 Plus-KAIST.

ON THE ASYMPTOTIC DYNAMICS OF THE VLASOV-YUKAWA-BOLTZMANN SYSTEM NEAR VACUUM

Sun-Ho CHOI, Seung-Yeal HA   

  1. 1. Department of Mathematical Sciences, KAIST, Daejeon 305-701, South Korea;
    2. Department of Mathematical Sciences and Research Institute of Mathematics Seoul National University, Seoul 151-747, South Korea
  • Received:2015-03-09 Online:2015-07-01 Published:2015-07-01
  • Supported by:

    The work of S.-Y. Ha is partially supported by a National Research Foundation of Korea Grant funded by the Korean Government (2014R1A2A205002096). The work of S.-H. Choi is supported by BK21 Plus-KAIST.

摘要:

In this paper, we study uniform L1-stability and asymptotic completeness of the Vlasov-Yukawa-Boltzmann (V-Y-B) system. For a sufficiently small and smooth initial data, we show that classical solutions exist globally and satisfy dispersion estimates, uniform L1-stability with respect to initial data and scattering type estimate. We show that the short range nature of interactions due to the Yukawa potential enables us to construct robust Lyapunov type functional to derive scattering states. In the zero mass limit of force carrier particles, we also show that the classical solutions to the V-Y-B system converge to that of the Vlasov-Poisson-Boltzmann (V-P-B) system in any finite time interval.

关键词: asymptotic completeness, collision operator, the Vlasov-Yukawa-Boltzmann system, uniform L1-stability

Abstract:

In this paper, we study uniform L1-stability and asymptotic completeness of the Vlasov-Yukawa-Boltzmann (V-Y-B) system. For a sufficiently small and smooth initial data, we show that classical solutions exist globally and satisfy dispersion estimates, uniform L1-stability with respect to initial data and scattering type estimate. We show that the short range nature of interactions due to the Yukawa potential enables us to construct robust Lyapunov type functional to derive scattering states. In the zero mass limit of force carrier particles, we also show that the classical solutions to the V-Y-B system converge to that of the Vlasov-Poisson-Boltzmann (V-P-B) system in any finite time interval.

Key words: asymptotic completeness, collision operator, the Vlasov-Yukawa-Boltzmann system, uniform L1-stability

中图分类号: 

  • 92D25