Estimates for the Boltzmann collision operator via radial symmetry and Fourier transform

Abstract

We extend the $L^p$-theory of the Boltzmann collision operator by using classical techniques based in the Carleman representation and Fourier analysis, allied to new ideas that exploit the radial symmetry of this operator. We are then able to greatly simplify existent technical proofs in this theory, extend the range, and obtain explicit sharp constants in some convolution-like inequalities for the gain part of the Boltzmann collision operator.

14 pages

References in corpus (3)

• Moment inequalities and high-energy tails for the Boltzmann equations with inelastic interactions
• Regularity theory for the spatially homogeneous Boltzmann equation with cut-off
• On the Boltzmann equation for diffusively excited granular media

Cited by in corpus (6)

• Convolution inequalities for the Boltzmann collision operator
• Distributional and classical solutions to the Cauchy Boltzmann problem for soft potentials with integrable angular cross section
• Well/Ill-posedness of the Boltzmann Equation with Soft Potential
• Well/ill-posedness bifurcation for the Boltzmann equation with constant collision kernel
• Convergence and error estimates for the Lagrangian based Conservative Spectral method for Boltzmann Equations
• Sharp regularizing estimates for the gain term of the Boltzmann collision operator