On the Cauchy problem of the Boltzmann and Landau equations with soft potentials
On the Cauchy problem of the Boltzmann and Landau equations with soft potentials
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DOI：
10.1090/s0033-569x-07-01053-8
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发表时间：
2007-04
影响因子：
0.8
通讯作者：
L. Hsiao;Hongjun Yu
中科院分区：
文献类型：
--
作者：
L. Hsiao;Hongjun Yu
，构造了具有全空间软势的Boltzmann和Landau方程在麦克斯韦方程组附近的全局经典解。全球解决方案的构建基于精细化的能源分析。我们的结果推广了Ukai和Asano （Publ.）的经典结果。Res. institute：数学。Sci. 18(1982), 477-519)扩展到玻尔兹曼方程的非常软势，并扩展了Caflisch （Comm. Math）中的经典结果。物理学74 (1980),97-107)；物理学报，2002,391-434)；老鼠。动力机械。al. 169(2003), 305-353)将库仑相互作用下的玻尔兹曼方程和朗道方程在周期盒中的整个空间。
, 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.