A BGK kinetic model with local velocity alignment forces

Young-Pil Choi; Seok-Bae Yun

doi:10.3934/nhm.2020024

Article Contents

2020, Volume 15, Issue 3: 389-404. Doi: 10.3934/nhm.2020024

This issue Previous Article Relative entropy method for the relaxation limit of hydrodynamic models Next Article Micro- and macroscopic modeling of crowding and pushing in corridors

A BGK kinetic model with local velocity alignment forces

Young-Pil Choi^1, , and
Seok-Bae Yun^2,

1.
Department of Mathematics, Yonsei University, Seoul 03722, Republic of Korea
2.
Department of Mathematics, Sungkyunkwan University, Suwon 440-746, Republic of Korea

^* Corresponding author: Young-Pil Choi
^* Corresponding author: Young-Pil Choi

Received: January 2020

Revised: May 2020

Early access: September 2020

Published: September 2020

Young-Pil Choi is supported by National Research Foundation of Korea(NRF) grants funded by the Korea government(MSIP) (No. 2017R1C1B2012918), POSCO Science Fellowship of POSCO TJ Park Foundation, and Yonsei University Research Fund of 2019-22-02. Seok-Bae Yun is supported by Samsung Science and Technology Foundation under Project Number SSTF-BA1801-02

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Abstract

The global Cauchy problem for a local alignment model with a relaxational inter-particle interaction operator is considered. More precisely, we consider the global-in-time existence of weak solutions of BGK model with local velocity-alignment term when the initial data have finite mass, momentum, energy, and entropy. The analysis involves weak/strong compactness based on the velocity moments estimates and several velocity-weighted $L^\infty$ estimates.

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Mathematics Subject Classification: 35Q20, 35Q92, 35Q83, 82B40.

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References

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