Quarterly of Applied Mathematics

On the Cauchy problem of the Boltzmann and Landau equations with soft potentials

Author(s): Ling Hsiao; Hongjun Yu
Journal: Quart. Appl. Math. 65 (2007), 281-315.
MSC (2000): Primary 35Q99; Secondary 35A05
Posted: April 25, 2007
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Abstract: Global classical solutions near Maxwellians are constructed for the Boltzmann and Landau equations with soft potentials in the whole space. The construction of global solutions is based on refined energy analysis. Our results generalize the classical results in Ukai and Asano (Publ. Res. Inst. Math. Sci. 18 (1982), 477-519) to the very soft potentials for the Boltzmann equation and also extend the classical results in Caflisch (Comm. Math. Phys. 74 (1980), 97-107), Guo (Comm. Math. Phys. 231 (2002), 391-434), and Guo (Arch. Rat. Mech. Anal. 169 (2003), 305-353) in the periodic box to the whole space for the Boltzmann equation and the Landau equation in the Coulomb interaction.

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Ling Hsiao
Affiliation: Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100080, People's Republic of China
Email: hsiaol@amss.ac.cn

Hongjun Yu
Affiliation: School of Mathematical Sciences, South China University of Technology, Guangzhou 510640, People's Republic of China
Email: yuhj2002@sina.com

PII: S0033-569X-07-01053-8
Keywords: Boltzmann equation, Landau equation, soft potentials, global solutions.
Received by editor(s): January 15, 2006
Posted: April 25, 2007
Copyright of article: Copyright 2007, Brown University
The copyright for this article reverts to public domain after 28 years from publication.

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