Solvability and blow-up criterion of the thermomechanical Cucker-Smale-Navier-Stokes equations in the whole domain

Kim, Jeongho; Zou, Weiyuan

doi:10.3934/krm.2020021

Cited by 3 publications

(1 citation statement)

References 26 publications

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“…The kinetic description of the TCS ensemble (1.5) has been analyzed recently in the literature. To name a few results: uniform-in-time mean-field limit [32], well-posedness and asymptotic behavior of the particle-fluid coupled systems [14,15,49], interaction with chemotactic movement [33] or propagation of mono-kinetic solutions [46] have been studied. We also refer [1,Section 4] for an overview of the TCS model.…”

Section: Introductionmentioning

confidence: 99%

Hydrodynamic limit of a coupled Cucker-Smale system with strong and weak internal variable relaxation

Kim,

Poyato,

Soler

2021

Preprint

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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.

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Section: Introductionmentioning

confidence: 99%

Hydrodynamic limit of a coupled Cucker-Smale system with strong and weak internal variable relaxation

Kim,

Poyato,

Soler

2021

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

The global existence of strong solutions to thermomechanical Cucker-Smale-Stokes equations in the whole domain

Zou

2024

Acta Math Sci

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Hydrodynamic limit of a coupled Cucker–Smale system with strong and weak internal variable relaxation

Kim

Poyato

Soler

2021

Math. Models Methods Appl. Sci.

View full text Add to dashboard Cite

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. While 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.

show abstract

Solvability and blow-up criterion of the thermomechanical Cucker-Smale-Navier-Stokes equations in the whole domain

Cited by 3 publications

References 26 publications

Hydrodynamic limit of a coupled Cucker-Smale system with strong and weak internal variable relaxation

Hydrodynamic limit of a coupled Cucker-Smale system with strong and weak internal variable relaxation

The global existence of strong solutions to thermomechanical Cucker-Smale-Stokes equations in the whole domain

Hydrodynamic limit of a coupled Cucker–Smale system with strong and weak internal variable relaxation

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