@misc{10481/70217,
year = {2021},
month = {1},
url = {http://hdl.handle.net/10481/70217},
abstract = {In this paper, we present the hydrodynamic limit of a multiscale system describing
the dynamics of two populations of agents with alignment interactions and the
effect of an internal variable. It consists of a kinetic equation coupled with an Euler-type
equation inspired by the thermomechanical Cucker–Smale (TCS) model. We propose a
novel drag force for the fluid-particle interaction reminiscent of Stokes’ law. Whilst the
macroscopic species is regarded as a self-organized background fluid that affects the kinetic
species, the latter is assumed sparse and does not affect the macroscopic dynamics.
We propose two hyperbolic scalings, in terms of a strong and weak relaxation regime of
the internal variable towards the background population. Under each regime, we prove
the rigorous hydrodynamic limit towards a coupled system composed of two Euler-type
equations. Inertial effects of momentum and internal variable in the kinetic species disappear
for strong relaxation, whereas a nontrivial dynamics for the internal variable appears
for weak relaxation. Our analysis covers both the case of Lipschitz and weakly singular
influence functions.},
organization = {European Research Council (ERC)	639638},
organization = {MECD (Spain)	FPU14/06304},
organization = {MINECO-Feder (Spain)	RTI2018-098850-B-I00},
organization = {Junta de Andalucia
European Commission	PY18-RT-2422	
A-FQM-311-UGR18},
organization = {Basic Science Research Program through the National Research Foundation of Korea (NRF) - Ministry of Science and ICT	NRF-2020R1A4A3079066},
publisher = {World Scientific},
keywords = {Flocking},
keywords = {Hydrodynamic limit},
keywords = {Kinetic model},
keywords = {Multiscale model},
keywords = {Thermomechanical Cucker-Smale model},
keywords = {Internal variable},
keywords = {Singular weights},
title = {Hydrodynamic limit of a coupled Cucker-Smale system with strong and weak internal variable relaxation},
doi = {10.1142/S0218202521400042},
author = {Kim, Jeongho and Poyato Sánchez, Jesús David and Soler Vizcaino, Juan Segundo},
}