Gevrey Smoothing Effect of Solutions to Non-Cutoff Boltzmann Equation for Soft Potential with Mild and Critical Singularity

2013/04/16 by Zhang, Teng-Fei, Yin, Zhaoyang
#35B65 #35Q20 #76P05 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1304.4388

Abstract

In this paper we study the Gevrey smoothing effect of solutions to the non-cutoff spatially homogeneous and inhomogeneous Boltzmann equation for soft potential. We consider the mild singularity case s<1/2 as we did in the previous work for spatially homogeneous case (J. Diff. Equ. 253(4) (2012), 1172-1190. DOI: 10.1016/j.jde.2012.04.023) and for spatially inhomogeneous case (arXiv:1304.2971), and try to extend the range of γ. We derive a new coercivity estimate for collision operator, using which we can obtain the Gevrey regularity for γ∈ (-5/2,0) improving the previous assumption γ∈ (-1-2s,0). Besides, we consider γ and s separately instead of viewing γ+2s as one untied quantity.

Related

• Gevrey Regularizing Effect for Solutions of the Non-Cutoff Boltzmann\n Equation in a Particular Case of Soft Potential with Critical Singularity
• Gevrey smoothing effect for the spatially inhomogeneous Boltzmann equations without cut-off
• Gevrey Regularity for Solutions of the Non-Cutoff Boltzmann Equation: Spatially Inhomogeneous Case
• Gevrey regularity of mild solutions to the non-cutoff Boltzmann equation
• Gevrey Smoothing Effect for Solutions of the Non-Cutoff Boltzmann Equation in Maxwellian Molecules Case