Regularity of solutions for spatially homogeneous Boltzmann equation without angular cutoff : non Maxwellian molecule type (Mathematical Analysis in Fluid and Gas Dynamics)
Regularity of solutions for spatially homogeneous Boltzmann equation without angular cutoff : non Maxwellian molecule type (Mathematical Analysis in Fluid and Gas Dynamics)
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DOI：
10.3934/krm.2008.1.453
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发表时间：
2008-08
期刊：
影响因子：
--
通讯作者：
Zhaohui Huo;Y. Morimoto;S. Ukai;Tong Yang
中科院分区：
文献类型：
--
作者：
Zhaohui Huo;Y. Morimoto;S. Ukai;Tong Yang
讨论了无角截断的空间齐次Boltzmann方程在修正的硬势和Debye-Yukawa势下解的正则性。当横截面的角奇异性为中等时，对于任意正时间，具有有限质量、能量和熵的弱解位于无限阶Sobolev空间中;而对于一般势，如果它具有任意阶矩，则位于Schwartz空间中.证明的主要内容是适当选择由伪微分算子组成的缓和算子，以及对Boltzmann碰撞算子和伪微分算子的缓和算子的精确估计.本文所提出的方法还提供了碰撞算子的一些新的估计。
The spatially homogeneous Boltzmann equation without angular cutoff is discussed on the regularity of solutions for the modified hard potential and Debye-Yukawa potential. When the angular singularity of the cross section is moderate, any weak solution having the finite mass, energy and entropy lies in the Sobolev space of infinite order for any positive time, while for the general potentials, it lies in the Schwartz space if it has moments of arbitrary order. The main ingredients of the proof are the suitable choice of the mollifiers composed of pseudo-differential operators and the sharp estimates of the commutators of the Boltzmann collision operator and pseudo-differential operators. The method developed here also provides some new estimates on the collision operator.