From BGK-alignment model to the pressured Euler-alignment system with singular communication weights

Young Pil Choi; Byung Hoon Hwang

doi:10.1016/j.jde.2023.10.010

From BGK-alignment model to the pressured Euler-alignment system with singular communication weights

Young Pil Choi, Byung Hoon Hwang

Department of Mathematics

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

4 Citations (Scopus)

Abstract

This paper is devoted to a rigorous derivation of the isentropic Euler-alignment system with singular communication weights ϕ_α(x)=|x|^−α for some α>0. We consider a kinetic BGK-alignment model consisting of a kinetic BGK-type equation with a singular Cucker-Smale alignment force. By taking into account a small relaxation parameter, which corresponds to the asymptotic regime of a strong effect from the BGK operator, we quantitatively derive the isentropic Euler-alignment system with pressure p(ρ)=ρ^γ, γ=1+[Formula presented] from that kinetic equation.

Original language	English
Pages (from-to)	363-412
Number of pages	50
Journal	Journal of Differential Equations
Volume	379
DOIs	https://doi.org/10.1016/j.jde.2023.10.010
Publication status	Published - 2024 Jan 15

Bibliographical note

Publisher Copyright:
© 2023 Elsevier Inc.

All Science Journal Classification (ASJC) codes

Analysis
Applied Mathematics

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10.1016/j.jde.2023.10.010

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title = "From BGK-alignment model to the pressured Euler-alignment system with singular communication weights",

abstract = "This paper is devoted to a rigorous derivation of the isentropic Euler-alignment system with singular communication weights ϕα(x)=|x|−α for some α>0. We consider a kinetic BGK-alignment model consisting of a kinetic BGK-type equation with a singular Cucker-Smale alignment force. By taking into account a small relaxation parameter, which corresponds to the asymptotic regime of a strong effect from the BGK operator, we quantitatively derive the isentropic Euler-alignment system with pressure p(ρ)=ργ, γ=1+[Formula presented] from that kinetic equation.",

keywords = "BGK model, Cucker-Smale model, Hydrodynamic limit, Isentropic Euler-alignment system, Relative entropy, Singular communication weight",

author = "Choi, {Young Pil} and Hwang, {Byung Hoon}",

note = "Publisher Copyright: {\textcopyright} 2023 Elsevier Inc.",

year = "2024",

month = jan,

day = "15",

doi = "10.1016/j.jde.2023.10.010",

language = "English",

volume = "379",

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AU - Choi, Young Pil

AU - Hwang, Byung Hoon

PY - 2024/1/15

Y1 - 2024/1/15

N2 - This paper is devoted to a rigorous derivation of the isentropic Euler-alignment system with singular communication weights ϕα(x)=|x|−α for some α>0. We consider a kinetic BGK-alignment model consisting of a kinetic BGK-type equation with a singular Cucker-Smale alignment force. By taking into account a small relaxation parameter, which corresponds to the asymptotic regime of a strong effect from the BGK operator, we quantitatively derive the isentropic Euler-alignment system with pressure p(ρ)=ργ, γ=1+[Formula presented] from that kinetic equation.

AB - This paper is devoted to a rigorous derivation of the isentropic Euler-alignment system with singular communication weights ϕα(x)=|x|−α for some α>0. We consider a kinetic BGK-alignment model consisting of a kinetic BGK-type equation with a singular Cucker-Smale alignment force. By taking into account a small relaxation parameter, which corresponds to the asymptotic regime of a strong effect from the BGK operator, we quantitatively derive the isentropic Euler-alignment system with pressure p(ρ)=ργ, γ=1+[Formula presented] from that kinetic equation.

KW - BGK model

KW - Cucker-Smale model

KW - Hydrodynamic limit

KW - Isentropic Euler-alignment system

KW - Relative entropy

KW - Singular communication weight

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DO - 10.1016/j.jde.2023.10.010

M3 - Article

AN - SCOPUS:85175197956

SN - 0022-0396

VL - 379

SP - 363

EP - 412

JO - Journal of Differential Equations

JF - Journal of Differential Equations

ER -

From BGK-alignment model to the pressured Euler-alignment system with singular communication weights

Abstract

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