Large-time decay of the soft potential relativisticBoltzmann equation in $\mathbb{R}^3_x$

Robert M. Strain; Keya Zhu

doi:10.3934/krm.2012.5.383

Article Contents

2012, Volume 5, Issue 2: 383-415. Doi: 10.3934/krm.2012.5.383

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Large-time decay of the soft potential relativistic Boltzmann equation in $\mathbb{R}^3_x$

Robert M. Strain^1, and
Keya Zhu^2,

1.
University of Pennsylvania, Department of Mathematics, David Rittenhouse Lab, 209 South 33rd Street, Philadelphia, PA 19104
2.
University of Pennsylvania, Department of Mathematics, David RittenhouseLab, 209 South 33rd Street, Philadelphia, PA 19104-6395

Received: November 30, 2011

Revised: January 31, 2012

Published: May 2012

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Abstract

For the relativistic Boltzmann equation in $\mathbb{R}^3_x$, this work proves the global existence, uniqueness, positivity, and optimal time convergence rates to the relativistic Maxwellian for solutions which start out sufficiently close under the general physical soft potential assumption proposed in 1988 [13].

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Mathematics Subject Classification: Primary: 76P05; Secondary: 83A05.

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References

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