Exponential decay for soft potentials near Maxwellian. Strain, R. M. & Guo, Y. Arch. Ration. Mech. Anal., 187(2):287–339, 2008.
Exponential decay for soft potentials near Maxwellian [pdf]Pdf  doi  abstract   bibtex   
Consider both soft potentials with angular cutoff and Landau collision kernels in the Boltzmann theory inside a periodic box. We prove that any smooth perturbation near a given Maxwellian approaches to zero at the rate of $e^{-λ t^{p}}$ for some $λ >0$ and $p∈ (0,1)$. Our method is based on an unified energy estimate with appropriate exponential velocity weight. Our results extend the classical Caflisch 1980 result to the case of very soft potential and Coulomb interactions.

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