Slow flocking dynamics of the Cucker-Smale ensemble with a chemotactic movement in a temperature field

Seung-Yeal Ha; Doheon Kim; Weiyuan Zou

doi:10.3934/krm.2020026

Article Contents

2020, Volume 13, Issue 4: 759-793. Doi: 10.3934/krm.2020026

This issue Previous Article Angular moments models for rarefied gas dynamics. Numerical comparisons with kinetic and Navier-Stokes equations Next Article Asymptotic flocking in the Cucker-Smale model with reaction-type delays in the non-oscillatory regime

Slow flocking dynamics of the Cucker-Smale ensemble with a chemotactic movement in a temperature field

1.
Department of Mathematical Sciences and Research Institute of Mathematics, Seoul National University, Seoul 08826 South Korea
2.
School of Mathematics, Korea Institute for Advanced Study, Seoul 02455, South Korea
3.
College of Mathematics and Physics, Beijing University of Chemical Technology, Beijing 100029, China

^* Corresponding author: Doheon Kim
^* Corresponding author: Doheon Kim

Communicated by Huijiang Zhao

Received: August 2019

Revised: February 2020

Published online: May 6, 2020

The work of S.-Y. Ha was supported by the National Research Foundation of Korea(NRF) Grant funded by the Korean Government(MSIP)(No.2017R1A5A1015626), and the work of D. Kim was supported by a KIAS Individual Grant (MG073901) at Korea Institute for Advanced Study, and the work of Weiyuan Zou is supported by the Fundamental Research Funds for the Central Universities ZY1937

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Abstract

We study slow flocking phenomenon arising from the dynamics of Cucker-Smale (CS) ensemble with chemotactic movements in a self-consistent temperature field. For constant temperature field, our situation reduces to the previous CS model with chemotactic movements. When a large CS ensemble with chemotactic movements is placed in a self-consistent temperature field, the dynamics of the CS ensemble can be effectively described by the kinetic thermodynamic CS (TCS) equation with chemotactic movements, which corresponds to the coupled collisional transport-reaction diffusion system. For the proposed coupled model, we provide a global solvability of strong solutions and their asymptotic flocking estimates which exhibit slow algebraic relaxation toward the flocking state. Our analytical results show that asymptotic flocking is robust with respect to a small perturbation of a constant temperature.

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Mathematics Subject Classification: Primary: 35B40, 35D35; Secondary: 70F45.

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References

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