Abstract
In this paper, we study the global existence and decay rates of the solutions near Maxwellian for non-linear Fokker–Planck equations in the whole space. The global existence is proved by combining uniform-in-time energy estimates with local solution constructed by Picard type iteration sequence. The decay rates of the nonlinear model is obtained by using the precise spectral analysis of the linearized Fokker–Planck operator as well as the energy method. The nonlinearity in the model brings new difficulty to the energy estimates, which is resolved by additional tailored weighted-in-v energy estimates suitable for Fokker–Planck operators.
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Acknowledgements
J. Liao would like thank Professor R. Alexandre for many valuable discussions on the model. This research is partially supported by Fundamental Research Funds for the Central Universities. X.F. Yang is supported by National Science Fund of China under the Grant 11171212 and the SJTU’s SMC Projection. The detailed suggestions from the anonymous referees are greatly appreciated.
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Liao, J., Wang, Q. & Yang, X. Global Existence and Decay Rates of the Solutions Near Maxwellian for Non-linear Fokker–Planck Equations. J Stat Phys 173, 222–241 (2018). https://doi.org/10.1007/s10955-018-2129-3
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DOI: https://doi.org/10.1007/s10955-018-2129-3