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Asymptotic Stability of the Relativistic Boltzmann Equation for the Soft Potentials

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Abstract

In this paper it is shown that unique solutions to the relativistic Boltzmann equation exist for all time and decay with any polynomial rate towards their steady state relativistic Maxwellian provided that the initial data starts out sufficiently close in \({L^\infty_\ell}\). If the initial data are continuous then so is the corresponding solution. We work in the case of a spatially periodic box. Conditions on the collision kernel are generic in the sense of Dudyński and Ekiel-Jeżewska (Commun Math Phys 115(4):607–629, 1985); this resolves the open question of global existence for the soft potentials.

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Authors and Affiliations

  1. Department of Mathematics, University of Pennsylvania, David Rittenhouse Lab, 209 South 33rd Street, Philadelphia, PA, 19104-6395, USA

    Robert M. Strain

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Correspondence to Robert M. Strain.

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Communicated by H. Spohn

The authors research was partially supported by the NSF grant DMS-0901463.

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Strain, R.M. Asymptotic Stability of the Relativistic Boltzmann Equation for the Soft Potentials. Commun. Math. Phys. 300, 529–597 (2010). https://doi.org/10.1007/s00220-010-1129-1

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