\(L^{\infty}\) estimates for the space-homogeneous Boltzmann equation
type: Item
instance of: scholarly article
title: \(L^{\infty}\) estimates for the space-homogeneous Boltzmann equation
zbMATH Open document ID: 0584.35090
DOI: 10.1007/BF01011586
author: Leif Arkeryd
published in: Journal of Statistical Physics
publication date: 1983-01-01T00:00:00Z
review text: The author studies the boundedness of solutions f of the initial-value problem for the space-homogeneous Boltzmann equation for inverse kth power forces, when \(k>5\), and under angular cutoff. The main result is that if the initial value is \(f_ 0\geq 0\) with \((1+| v|^ 2)f_ 0\in L^ 1,\) and \((1+| v|)^ sf_ 0\in L^{\infty}\) for some \(s>2\), then \((1+| v|)^{s'}f_ t\in L^{\infty}\) for \(t>0\) and \( \sup_{v,t}(1+| v|)^{s'}f(v,t)<\infty\) for any s'\(\leq s\) when \(s\leq 5\), and any \(s'<s\) if \(s>5\).
Mathematics Subject Classification ID: 35Q99
Mathematics Subject Classification ID: 35G25
Mathematics Subject Classification ID: 35B35
zbMATH DE Number: 3935634
zbMATH Keywords: nonlinear Boltzmann equation
zbMATH Keywords: boundedness
zbMATH Keywords: initial-value problem
zbMATH Keywords: space- homogeneous Boltzmann equation
MaRDI profile type: Publication
cites work: On the Boltzmann equation. II: The full initial value problem
cites work: Q3242076
cites work: Global boundedness of moments of solutions of the Boltzmann equation for forces of infinite range
full work available at URL: https://doi.org/10.1007/bf01011586
OpenAlex ID: W1974110902
description: scientific article; zbMATH DE number 3935634