Optimal convergence rates of classical solutions for Vlasov-Poisson-Boltzmann system
type: Item
instance of: scholarly article
title: Optimal convergence rates of classical solutions for Vlasov-Poisson-Boltzmann system
zbMATH Open document ID: 1233.35040
author: Tong Yang
author: Hongjun Yu
published in: Communications in Mathematical Physics
publication date: 2011-02-14T00:00:00Z
review text: The paper is concerned with a system of two species of oppositely charged particles which interact through collisions in the self-induced electric field. The dynamics is modeled by a Vlasov-Poisson-Boltzmann system. The main aim of the authors is that of studying the optimal time decay of the system near the equilibrium state which is a global Maxwellian in the whole space. The main ingredient in the analysis is the generalization of the compensating function introduced by Kawashima to a two-species system. Some refined energy estimates are used in order to obtain the time convergence rates which are optimal in the sense that they are the same as those for the linearized system.
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35Q20
Mathematics Subject Classification ID: 35Q83
Mathematics Subject Classification ID: 35B35
Mathematics Subject Classification ID: 35B45
zbMATH DE Number: 5851407
zbMATH Keywords: compensating function
zbMATH Keywords: energy method
zbMATH Keywords: optimal time decay
reviewed by: Giovanni Mascali
MaRDI profile type: Publication
full work available at URL: s00220-010-1142-4
OpenAlex ID: W2063741304
cites work: The mathematical theory of dilute gases
cites work: Q5816506
cites work: Optimal time decay of the Vlasov-Poisson-Boltzmann system in \({\mathbb R^3}\)
cites work: Optimal decay estimates on the linearized Boltzmann equation with time dependent force and their applications
cites work: Decay estimates for the compressible Navier-Stokes equations in unbounded domains
cites work: On long time asymptotics of the vlasov—poisson—boltzmann equation
cites work: Q4868584
cites work: Decay of the linearized Boltzmann-Vlasov system
cites work: Perturbation of essential spectra of evolution operators and the Vlasov-Poisson-Boltzmann system
cites work: The Vlasov‐Poisson‐Boltzmann system near Maxwellians
cites work: The Vlasov-Maxwell-Boltzmann system near Maxwellians
cites work: The Boltzmann equation in the whole space
cites work: Boltzmann diffusive limit beyond the Navier‐Stokes approximation
cites work: The Boltzmann equation and thirteen moments
cites work: Q4011221
cites work: Energy method for Boltzmann equation
cites work: Boltzmann equation: micro-macro decompositions and positivity of shock profiles
cites work: On the initial boundary value problem for the Vlasov-Poisson-Boltzmann system
cites work: The Vlasov-Maxwell-Boltzmann system in the whole space
cites work: On the existence of global solutions of mixed problem for non-linear Boltzmann equation
cites work: Q4409400
cites work: Hypocoercivity of the relativistic Boltzmann and Landau equations in the whole space
cites work: Optimal convergence rates of Landau equation with external forcing in the whole space
cites work: Cauchy problem for the Vlasov-Poisson-Boltzmann system
cites work: Global existence of classical solutions to the Vlasov-Poisson-Boltzmann system
cites work: A new energy method for the Boltzmann equation
cites work: Stability of the Vlasov-Poisson-Boltzmann system in \(\mathbb R^3\)
DOI: 10.1007/S00220-010-1142-4
description: scientific article; zbMATH DE number 5851407