Smoothing effect of weak solutions for the spatially homogeneous Boltzmann Equation without angular cutoff
Smoothing effect of weak solutions for the spatially homogeneous Boltzmann Equation without angular cutoff
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DOI：
10.1215/21562261-1625154
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发表时间：
2011-04
影响因子：
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通讯作者：
Radjesvarane Alexandre;Y. Morimoto;S. Ukai;Chao-Jiang Xu;Tong Yang
中科院分区：
文献类型：
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作者：
Radjesvarane Alexandre;Y. Morimoto;S. Ukai;Chao-Jiang Xu;Tong Yang
本文考虑无角截断的空间齐次Boltzmann方程。我们证明了具有有限阶矩的Cauchy问题的每一个L^1 $弱解在正时间上都具有速度变量的C^\infty$正则性.
In this paper, we consider the spatially homogeneous Boltzmann equation without angular cutoff. We prove that every $L^1$ weak solution to the Cauchy problem with finite moments of all order acquires the $C^\infty$ regularity in the velocity variable for the positive time.