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The Boltzmann equation with a soft potential

II. Nonlinear, spatially-periodic

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Abstract

The results of Part I are extended to include linear spatially periodic problems-solutions of the initial value are shown to exist and decay like\(e^{ - \lambda t^\beta } \). Then the full non-linear Boltzmann equation with a soft potential is solved for initial data close to equilibrium. The non-linearity is treated as a perturbation of the linear problem, and the equation is solved by iteration.

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References

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Authors and Affiliations

  1. Department of Mathematics, Stanford University, 94305, Stanford, CA, USA

    Russel E. Caflisch

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  1. Russel E. Caflisch
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Communicated by E. Lieb

Supported by the National Science Foundation under Grant Nos. MCS78-09525 and MCS76-07039 and by the United States Army under Contract No. DAAG29-75-C-0024

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Caflisch, R.E. The Boltzmann equation with a soft potential. Commun.Math. Phys. 74, 97–109 (1980). https://doi.org/10.1007/BF01197752

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  • DOI: https://doi.org/10.1007/BF01197752

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