Hydrodynamic limit of the kinetic thermomechanical Cucker-Smale model in a strong local alignment regime

Moon-Jin Kang; Seung-Yeal Ha; Jeongho Kim; Woojoo Shim

doi:10.3934/cpaa.2020057

Article Contents

2020, Volume 19, Issue 3: 1233-1256. Doi: 10.3934/cpaa.2020057

This issue Previous Article Bifurcation and stability of a two-species diffusive Lotka-Volterra model Next Article Stochastic functional Hamiltonian system with singular coefficients

Hydrodynamic limit of the kinetic thermomechanical Cucker-Smale model in a strong local alignment regime

1.
Department of Mathematics and Research Institute of Natural Sciences, Sookmyung Women's University, Seoul 04310, Republic of Korea
2.
Department of Mathematical Sciences and Research Institute of Mathematics, Seoul National University, Seoul 08826, Republic of Korea
3.
Institute of New Media and Communications, Seoul National University, Seoul 08826, Republic of Korea
4.
Department of Mathematical Sciences, Seoul National University, Seoul 08826, Republic of Korea

^* Corresponding author
^* Corresponding author

Received: September 30, 2018

Revised: July 31, 2019

Published: February 2020

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Abstract

We present a hydrodynamic limit from the kinetic thermomechanical Cucker-Smale (TCS) model to the hydrodynamic Cucker-Smale (CS) model in a strong local alignment regime. For this, we first provide a global existence of weak solution, and flocking dynamics for classical solution to the kinetic TCS model with local alignment force. Then we consider one-parameter family of well-prepared initial data to the kinetic TCS model in which the temperature tends to common constant value determined by initial datum, as singular parameter $ \varepsilon $ tends to zero. In a strong local alignment regime, the limit model is the hydrodynamic CS model in [8]. To verify this hydrodynamic limit rigorously, we adopt the technique introduced in [5] which combines the relative entropy method together with the 2-Wasserstein metric.

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Mathematics Subject Classification: Primary: 92D25, 74A25; Secondary: 76N10.

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References

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