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December  2009, 2(4): 647-666. doi: 10.3934/krm.2009.2.647

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

Nadia Lekrine 1, and  Chao-Jiang Xu 1,

1. 

Université de Rouen, UMR 6085-CNRS, Mathématiques, Avenue de l’Université, BP.12, 76801 Saint Etienne du Rouvray, France

Received  April 2009 Revised  August 2009 Published  October 2009

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.
Keywords: Non-cutoff Kac's equation, Boltzmann equation, Gevrey regularizing effect, Cauchy problem, Fourier analysis..
Mathematics Subject Classification: 35A05, 35B65,35D10, 42A38, 60H07, 82B4.
Citation: Nadia Lekrine, Chao-Jiang Xu. Gevrey regularizing effect of the Cauchy problem for non-cutoff homogeneous Kac's equation. Kinetic & Related Models, 2009, 2 (4) : 647-666. doi: 10.3934/krm.2009.2.647
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