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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Caflisch, R.: Commun. Math. Phys.74, 1–95 (1980)
Ellis, R., Pinsky, M.: The first and second fluid approximations to the linearized Boltzmann equation. J. Math. Pures Appl.54, 125–156 (1975)
Grad, H.: Asymptotic convergence of the Navier-Stokes and the nonlinear Boltzmann equations. Proc. Symp. Appl. Math.17, 154–183 (1965)
Schecter, M.: On the essential spectrum of an arbitrary operator. J. Math. Anal. Appl.13, 205–215 (1966)
Ukai, S.: On the existence of global solutions of mixed problems for non-linear Boltzmann equations. Proc. Jpn. Acad.50, 179–184 (1974)
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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