A BGK kinetic model with local velocity alignment forces

Young-Pil Choi; Seok-Bae Yun; Young-Pil Choi; Seok-Bae Yun

doi:10.3934/nhm.2020024

Networks and Heterogeneous Media

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

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A BGK kinetic model with local velocity alignment forces

Young-Pil Choi ^{1
,
,},
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

Received: 01 January 2020 Revised: 01 May 2020 Published: 09 September 2020
35Q20, 35Q92, 35Q83, 82B40

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.
- Kinetic flocking model,
- BGK model of Boltzmann equation,
- weak solution
Citation: Young-Pil Choi, Seok-Bae Yun. A BGK kinetic model with local velocity alignment forces[J]. Networks and Heterogeneous Media, 2020, 15(3): 389-404. doi: 10.3934/nhm.2020024

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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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