Macroscopic regularity for the relativistic Boltzmann equation with initial singularities

Yan Yong; Weiyuan Zou

doi:10.3934/krm.2019036

Article Contents

2019, Volume 12, Issue 5: 945-967. Doi: 10.3934/krm.2019036

This issue Previous Article Next Article Local sensitivity analysis and spectral convergence of the stochastic Galerkin method for discrete-velocity Boltzmann equations with multi-scales and random inputs

Macroscopic regularity for the relativistic Boltzmann equation with initial singularities

Yan Yong^1, and
Weiyuan Zou^2, ,

1.
College of Science, University of Shanghai for Science and Technology, Shanghai 200093, China
2.
College of Mathematics and Physics, Beijing University of Chemical Technology, Beijing 100029, China

^* Corresponding author: Weiyuan Zou^*
^* Corresponding author: Weiyuan Zou^*

Received: December 31, 2017

Revised: October 31, 2018

Published: July 2019

The second author is supported by the Fundamental Research Funds for the Central Universities ZY1937.

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Abstract

In this paper, it is proved that the macroscopic parts of the relativistic Boltzmann equation will be continuous, even though the macroscopic components are discontinuity initially. The Lorentz transformation plays an important role to prove the continuity of nonlinear term.

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Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

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References

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