Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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

   
 
 

 

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


Authors: Ling Hsiao and Hongjun Yu
Journal: Quart. Appl. Math. 65 (2007), 281-315
MSC (2000): Primary 35Q99; Secondary 35A05
DOI: https://doi.org/10.1090/S0033-569X-07-01053-8
Published electronically: April 25, 2007
MathSciNet review: 2330559
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Quarterly of Applied Mathematics with MSC (2000): 35Q99, 35A05

Retrieve articles in all journals with MSC (2000): 35Q99, 35A05


Additional Information

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

DOI: https://doi.org/10.1090/S0033-569X-07-01053-8
Keywords: Boltzmann equation, Landau equation, soft potentials, global solutions.
Received by editor(s): January 15, 2006
Published electronically: April 25, 2007
Article copyright: © Copyright 2007 Brown University
The copyright for this article reverts to public domain 28 years after publication.

American Mathematical Society