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

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

doi:10.1112/jlms.70088

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

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

Research output: Contribution to journal › Article › peer-review

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
Article number	e70088
Journal	Journal of the London Mathematical Society
Volume	111
Issue number	2
DOIs	https://doi.org/10.1112/jlms.70088
Publication status	Published - 2025 Feb

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© 2025 The Author(s). The publishing rights in this article are licensed to the London Mathematical Society under an exclusive licence.

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1112/jlms.70088

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

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