Rigorous derivation of the Euler-alignment model with singular communication weights from a kinetic Fokker-Planck-alignment model

Young Pil Choi; Jeongho Kim

doi:10.1142/S0218202523500021

Rigorous derivation of the Euler-alignment model with singular communication weights from a kinetic Fokker-Planck-alignment model

Young Pil Choi, Jeongho Kim

Department of Mathematics

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

Abstract

In this paper, we present a rigorous derivation of the isothermal Euler-alignment model with singular communication weights. We consider a hydrodynamic limit of a kinetic Fokker-Planck-alignment model, which is the nonlinear Fokker-Planck equation with the Cucker-Smale alignment force. Our analysis is based on the estimate of relative entropy between macroscopic quantities, together with careful analysis on the singular communication weights.

Original language	English
Pages (from-to)	31-65
Number of pages	35
Journal	Mathematical Models and Methods in Applied Sciences
Volume	33
Issue number	1
DOIs	https://doi.org/10.1142/S0218202523500021
Publication status	Published - 2023 Jan 1

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© 2023 World Scientific Publishing Company.

All Science Journal Classification (ASJC) codes

Modelling and Simulation
Applied Mathematics

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10.1142/S0218202523500021

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Rigorous derivation of the Euler-alignment model with singular communication weights from a kinetic Fokker-Planck-alignment model

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