Uniform $L^1$-stability of the relativistic Boltzmann equation nearvacuum

Seung-Yeal Ha; Eunhee Jeong; Robert M. Strain

doi:10.3934/cpaa.2013.12.1141

Article Contents

2013, Volume 12, Issue 2: 1141-1161. Doi: 10.3934/cpaa.2013.12.1141

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Uniform $L^1$-stability of the relativistic Boltzmann equation near vacuum

1.
Department of Mathematical Sciences, Seoul National University, Seoul 151-747
2.
University of Pennsylvania, Department of Mathematics, David Rittenhouse Lab, 209 South 33rd Street, Philadelphia, PA 19104-6395

Received: August 31, 2011

Revised: January 31, 2012

Published: February 2013

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Abstract

We present the uniform $L^1$-stability estimate for the relativistic Boltzmann equation near vacuum. For this, we explicitly construct a relativistic counterpart of the nonlinear functional which is a linear combination of $L^1$-distance and a collision potential. This functional measures the $L^1$-distance between two continuous mild solutions. When the initial data is sufficiently small and decays exponentially fast, we show that the functional satisfies the uniform stability estimate leading to the uniform $L^1$-stability estimate with respect to initial data.

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Mathematics Subject Classification: 35Q35.

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