Gevrey smoothing effect of solutions for spatially homogeneous nonlinear Boltzmann equation without angular cutoff

Abstract

There have been extensive studies on the regularizing effect of solutions to the Boltzmann equation without angular cutoff assumption, for both spatially homogeneous and inhomogeneous cases, by noticing the fact that non cutoff Boltzmann collision operator behaves like the fractional power of the Laplace operator. As a further study on the problem in the spatially homogeneous situation, in this paper, we consider the Gevrey regularity of C ∞ solutions with the Maxwellian decay to the Cauchy problem of spatially homogeneous Boltzmann equation for modified hard potentials, by using analytic techniques developed in Alexandre et al. (J Funct Anal 255:2013–2066, 2008; Arch Ration Mech Anal, doi: 10.1007/s00205-010-0290-1 , 2010), Huo et al. (Kinet Relat Models 1:453–489, 2008) and Morimoto et al. (Discrete Contin Dyn Syst Ser A 24:187–212, 2009).