Existence of weak solutions and long-time asymptotics for hydrodynamic model of swarming

Nilasis Chaudhuri; Young-Pil Choi; Oliver Tse; Ewelina Zatorska

doi:10.48550/arXiv.2402.07130

Existence of weak solutions and long-time asymptotics for hydrodynamic model of swarming

Nilasis Chaudhuri, Young-Pil Choi, Oliver Tse, Ewelina Zatorska

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Abstract

We consider a one-dimensional hydrodynamic model featuring nonlocal attraction-repulsion interactions and singular velocity alignment. We introduce a two-velocity reformulation and the corresponding energy-type inequality, in the spirit of the Bresch-Desjardins estimate. We identify a dependence between the communication weight and interaction kernel and between the pressure and viscosity term allowing for this inequality to be uniform in time. It is then used to study long-time asymptotics of solutions.

Original language	English
Publisher	arXiv.org
Number of pages	37
Volume	2402.07130
DOIs	https://doi.org/10.48550/arXiv.2402.07130
Publication status	Published - 11 Feb 2024

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math.AP

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2402.07130v1Final published version, 378 KBLicence: CC BY

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AU - Tse, Oliver

AU - Zatorska, Ewelina

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N2 - We consider a one-dimensional hydrodynamic model featuring nonlocal attraction-repulsion interactions and singular velocity alignment. We introduce a two-velocity reformulation and the corresponding energy-type inequality, in the spirit of the Bresch-Desjardins estimate. We identify a dependence between the communication weight and interaction kernel and between the pressure and viscosity term allowing for this inequality to be uniform in time. It is then used to study long-time asymptotics of solutions.

AB - We consider a one-dimensional hydrodynamic model featuring nonlocal attraction-repulsion interactions and singular velocity alignment. We introduce a two-velocity reformulation and the corresponding energy-type inequality, in the spirit of the Bresch-Desjardins estimate. We identify a dependence between the communication weight and interaction kernel and between the pressure and viscosity term allowing for this inequality to be uniform in time. It is then used to study long-time asymptotics of solutions.

KW - math.AP

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BT - Existence of weak solutions and long-time asymptotics for hydrodynamic model of swarming

PB - arXiv.org

ER -

Existence of weak solutions and long-time asymptotics for hydrodynamic model of swarming

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