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arXiv · 1201.2048

Gevrey regularity of spatially homogeneous Boltzmann equation without cutoff

Teng-Fei Zhang·Zhaoyang Yin
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Abstract

In this paper, we study the Gevrey regularity of spatially homogeneous Boltzmann equation without angular cutoff. We prove the propagation of Gevrey regularity for $C^\infty$ solutions with the Maxwellian decay to the Cauchy problem of spatially homogeneous Boltzmann equation. The idea we use here is based on the framework of Morimoto's recent paper (See Morimoto: J. Pseudo-Differ. Oper. Appl. (2010) 1: 139-159, DOI:10.1007/s11868-010-0008-z), but we extend the range of the index $γ$ satisfying $γ+ 2s \in (-1,1)$, $s\in (0,1/2)$ and in this case we consider the kinetic factor in the form of $Φ(v)=|v|^γ$ instead of $\la v \ra ^γ$ as Morimoto did before.

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Teng-Fei Zhang, Zhaoyang Yin. 2012-01-10. Gevrey regularity of spatially homogeneous Boltzmann equation without cutoff. https://arxiv.org/abs/1201.2048

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