Regularity of Non-cutoff Boltzmann Equation with Hard Potential

Abstract

This article proves the regularity for the Boltzmann equation without angular cutoff with hard potential. By sharpening the coercivity and upper bound estimate on the collision operator, analyzing the Poisson bracket between the transport operator and some weighted pseudo-differential operator, we prove the regularizing effect in space and velocity variables when the initial data has mild regularity.

arXiv commentarXiv admin note: text overlap with arXiv:2004.07794

References in corpus (8)

• Global Classical Solutions of the Boltzmann Equation without Angular Cut-off
• Global Strong Solutions of the Boltzmann Equation without Angular Cut-off
• Regularizing effect and local existence for non-cutoff Boltzmann equation
• Spectral gap and coercivity estimates for linearized Boltzmann collision operators without angular cutoff
• The Boltzmann equation without angular cutoff in the whole space: III, Qualitative properties of solutions
• Sharp anisotropic estimates for the Boltzmann collision operator and its entropy production
• Gevrey smoothing for weak solutions of the fully nonlinear homogeneous Boltzmann and Kac equations without cutoff for Maxwellian molecules
• Strong smoothing for the non-cutoff homogeneous Boltzmann equation for Maxwellian molecules with Debye-Yukawa type interaction

Cited by in corpus (3)

• Regularity of the Vlasov-Poisson-Boltzmann System without angular cutoff
• Global Existence of Non-cutoff Boltzmann Equation in Weighted Sobolev Space
• Global Regularity of the Vlasov-Poisson-Boltzmann System Near Maxwellian Without Angular Cutoff for Soft Potential