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arXiv · 0911.4279

Gevrey regularizing effect of the Cauchy problem for non-cutoff homogeneous Kac's equation

Nadia Lekrine·Chao-Jiang Xu
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Abstract

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.

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Nadia Lekrine, Chao-Jiang Xu. 2009-11-22. Gevrey regularizing effect of the Cauchy problem for non-cutoff homogeneous Kac's equation. https://arxiv.org/abs/0911.4279

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