Acta mathematica scientia, Series B >
ON THE ASYMPTOTIC DYNAMICS OF THE VLASOV-YUKAWA-BOLTZMANN SYSTEM NEAR VACUUM
Received date: 2015-03-09
Online 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.
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.
Sun-Ho CHOI , Seung-Yeal HA . ON THE ASYMPTOTIC DYNAMICS OF THE VLASOV-YUKAWA-BOLTZMANN SYSTEM NEAR VACUUM[J]. Acta mathematica scientia, Series B, 2015 , 35(4) : 887 -905 . DOI: 10.1016/S0252-9602(15)30027-8
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