Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X

   
 
 

 

Global existence and stability of mild solutions to the Boltzmann system for gas mixtures


Authors: Seung-Yeal Ha, Se Eun Noh and Seok Bae Yun
Journal: Quart. Appl. Math. 65 (2007), 757-779
MSC (2000): Primary 35Q40
DOI: https://doi.org/10.1090/S0033-569X-07-01068-6
Published electronically: August 28, 2007
MathSciNet review: 2370359
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Abstract: We present the global existence and stability of mild solutions to the Boltzmann system with inverse power molecular interactions for a binary gas mixture, when initial data are sufficiently small and decay exponentially in phase space. For the existence and stability of mild solutions, we employ a modified Kaniel-Shinbrot's scheme and a weighted nonlinear functional approach. Time-asymptotic convergence toward the free molecular motion is established using a weighted collision potential, and we show that the weighted $ L^1$-distance between two mild solutions is uniformly controlled by that of initial data.


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Additional Information

Seung-Yeal Ha
Affiliation: Department of Mathematical Sciences, Seoul National University, Seoul 151-747, Korea
Email: syha@math.snu.ac.kr

Se Eun Noh
Affiliation: Department of Mathematical Sciences, Seoul National University, Seoul 151-747, Korea
Email: senoh@math.snu.ac.kr

Seok Bae Yun
Affiliation: Department of Mathematical Sciences, Seoul National University, Seoul 151-747, Korea
Email: sbyun@math.snu.ac.kr

DOI: https://doi.org/10.1090/S0033-569X-07-01068-6
Received by editor(s): February 27, 2007
Published electronically: August 28, 2007
Article copyright: © Copyright 2007 Brown University
The copyright for this article reverts to public domain 28 years after publication.

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