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

Hsiao, Ling; Yu, Hongjun

doi:10.1090/S0033-569X-07-01053-8

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
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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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