Gevrey regularizing effect of the Cauchy problem for non-cutoff
homogeneous Kac's equation
Nadia Lekrine - Université de Rouen, UMR 6085-CNRS, Mathématiques, Avenue de l’Université, BP.12, 76801 Saint Etienne du Rouvray, France (email)
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.
Keywords: Non-cutoff Kac's equation, Boltzmann equation, Gevrey
regularizing effect, Cauchy problem, Fourier analysis.
Received: April 2009; Revised: August 2009; Published: October 2009.
2011 Impact Factor.677