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Exponential Decay for Soft Potentials near Maxwellian

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Abstract

We 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 zero at the rate of \(e^{-\lambda t^{p}}\) for some λ  > 0 and 0 < p < 1. Our method is based on an unified energy estimate with appropriate exponential velocity weight. Our results extend the classical result Caflisch of [2] to the case of very soft potential and Coulomb interactions, and also improve the recent “almost exponential” decay results by [5, 14].

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Authors and Affiliations

  1. Department of Mathematics, Harvard University, Cambridge, MA, 02138, USA

    Robert M. Strain

  2. Division of Applied Mathematics, Brown University, Providence, RI, 02912, USA

    Yan Guo

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  1. Robert M. Strain
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  2. Yan Guo
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Correspondence to Robert M. Strain.

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Communicated by P.-L. Lions

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Strain, R.M., Guo, Y. Exponential Decay for Soft Potentials near Maxwellian. Arch Rational Mech Anal 187, 287–339 (2008). https://doi.org/10.1007/s00205-007-0067-3

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  • DOI: https://doi.org/10.1007/s00205-007-0067-3

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