Probability approaches to spatially homogeneous Boltzmann equations

Xicheng Zhang; Xianwen Zhang

doi:10.1080/07362990701567231

Probability approaches to spatially homogeneous Boltzmann equations

Xicheng Zhang^*
, Xianwen Zhang^*

^*Corresponding author for this work

Huazhong University of Science and Technology

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

This article is devoted to the study of the probability measure solutions to the spatially homogeneous Boltzmann equations. First, we provide a measure theoretical treatment to the Boltzmann collision operator. Then, the existence results both for the cutoff kernels and the non cutoff ones are established in the sense of measure-valued solutions. We also give a partial uniqueness result and some estimates for pth order moment (p2).

Original language	English
Pages (from-to)	1129-1150
Number of pages	22
Journal	Stochastic Analysis and Applications
Volume	25
Issue number	6
DOIs	https://doi.org/10.1080/07362990701567231
Publication status	Published - Nov 2007
Externally published	Yes

Keywords

Boltzmann equation
Measure solution
Probability approach

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10.1080/07362990701567231

Cite this

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title = "Probability approaches to spatially homogeneous Boltzmann equations",

abstract = "This article is devoted to the study of the probability measure solutions to the spatially homogeneous Boltzmann equations. First, we provide a measure theoretical treatment to the Boltzmann collision operator. Then, the existence results both for the cutoff kernels and the non cutoff ones are established in the sense of measure-valued solutions. We also give a partial uniqueness result and some estimates for pth order moment (p2).",

keywords = "Boltzmann equation, Measure solution, Probability approach",

author = "Xicheng Zhang and Xianwen Zhang",

year = "2007",

month = nov,

doi = "10.1080/07362990701567231",

language = "English",

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AU - Zhang, Xicheng

AU - Zhang, Xianwen

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AB - This article is devoted to the study of the probability measure solutions to the spatially homogeneous Boltzmann equations. First, we provide a measure theoretical treatment to the Boltzmann collision operator. Then, the existence results both for the cutoff kernels and the non cutoff ones are established in the sense of measure-valued solutions. We also give a partial uniqueness result and some estimates for pth order moment (p2).

KW - Boltzmann equation

KW - Measure solution

KW - Probability approach

UR - https://www.scopus.com/pages/publications/35648950635

U2 - 10.1080/07362990701567231

DO - 10.1080/07362990701567231

M3 - Article

AN - SCOPUS:35648950635

SN - 0736-2994

VL - 25

SP - 1129

EP - 1150

JO - Stochastic Analysis and Applications

JF - Stochastic Analysis and Applications

IS - 6

ER -

Probability approaches to spatially homogeneous Boltzmann equations

Abstract

Keywords

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