Uniform stability of the Boltzmann equation with an external force near vacuum

Zhigang Wu; Wenjun Wang

doi:10.3934/cpaa.2015.14.811

Article Contents

2015, Volume 14, Issue 3: 811-823. Doi: 10.3934/cpaa.2015.14.811

This issue Previous Article Differential Harnack estimates for backward heat equations with potentials under geometric flows Next Article Standing wave concentrating on compact manifolds for nonlinear Schrödinger equations

Uniform stability of the Boltzmann equation with an external force near vacuum

Zhigang Wu^1, and
Wenjun Wang^2,

1.
Department of Applied Mathematics, Donghua University, Shanghai 201620
2.
College of Science, University of Shanghai for Science and Technology, Shanghai 200093

Received: August 2010

Revised: January 2015

Published: May 2015

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Abstract

The temporal uniform $L^1(x,v)$ stability of mild solutions for the Boltzmann equation with an external force is considered. We give a unified proof of the stability for two kinds of the forces. Firstly, we extend the soft potential case in [9] to both soft and hard cases. Secondly, we weaken the condition on the force in [13]. Furthermore, we give some new examples satisfying the constructive conditions on the force in [11].

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Mathematics Subject Classification: Primary: 35Q20; Secondary: 82C40.

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References

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