Gevrey regularizing effect of the Cauchy problem for non-cutoff homogeneous Kac's equation
Gevrey regularizing effect of the Cauchy problem for non-cutoff homogeneous Kac's equation
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DOI：
10.3934/krm.2009.2.647
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发表时间：
2009-10
影响因子：
1
通讯作者：
Nadia Lekrine;Chao-Jiang Xu
中科院分区：
文献类型：
--
作者：
Nadia Lekrine;Chao-Jiang Xu
本文考虑了具有非截断截面的空间齐次Kac方程。我们证明了Cauchy问题的弱解在正时间下属于Gevrey类。这是非光滑初始数据的Gevrey正则化效应。证明依赖于Kac算子的傅立叶分析和指数型软化器。
In this work, we consider a spatially homogeneous Kac's equation with a non cutoff cross section. We prove that the weak solution of the Cauchy problem is in the Gevrey class for positive time. This is a Gevrey regularizing effect for non smooth initial datum. The proof relies on the Fourier analysis of Kac's operators and on an exponential type mollifier.