Uniqueness of solutionsfor the non-cutoff Boltzmann equationwith soft potential

Radjesvarane Alexandre; Yoshinori Morimoto; Seiji Ukai; Chao-Jiang Xu; Tong Yang

doi:10.3934/krm.2011.4.919

Article Contents

2011, Volume 4, Issue 4: 919-934. Doi: 10.3934/krm.2011.4.919

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Uniqueness of solutions for the non-cutoff Boltzmann equation with soft potential

1.
Department of Mathematics, Shanghai Jiao Tong University, Shanghai, 200240
2.
Graduate School of Human and Environmental Studies, Kyoto University, Kyoto, 606-8501
3.
17-26 Iwasaki, Hodogaya, Yokohama 240-0015
4.
School of Mathematics, Wuhan University, 430072, Wuhan
5.
Department of Mathematics, City University of Hong Kong, Kowloon, Hong Kong

Received: April 30, 2011

Revised: May 31, 2011

Published: November 2011

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Abstract

In this paper, we consider the Cauchy problem for the non-cutoff Boltzmann equation in the soft potential case. By using a singular change of velocity variables before and after collision, we prove the uniqueness of weak solutions to the Cauchy problem in the space of functions with polynomial decay in the velocity variable.

Keywords:

Mathematics Subject Classification: 35A05, 35B65, 35D10, 35H20, 76P05, 82C40.

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References

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