Existence of weak solutions and long‐time asymptotics for hydrodynamic model of swarming
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.
Authors
- Oliver Tse (ORCID: https://orcid.org/0000-0001-7577-3110)
- Nilasis Chaudhuri (ORCID: https://orcid.org/0000-0003-0384-9301)
- Ewelina Zatorska (ORCID: https://orcid.org/0000-0003-0468-4975)
- Young‐Pil Choi
Institutions
- Yonsei University (KR)
- University of Warwick (GB)
- University of Warsaw (PL)
- Eindhoven University of Technology (NL)
Publication Details
- Journal
- Journal of the London Mathematical Society
- Published
- 2025-02-01
- DOI
- https://doi.org/10.1112/jlms.70088
- Citations
- 1
- Primary Topic
- Aquatic and Environmental Studies
- Type
- article
- Field-Weighted Citation Impact
- 1.67
Funders
- Yonsei University
- Nederlandse Organisatie voor Wetenschappelijk Onderzoek
- National Research Foundation of Korea
- Uniwersytet Warszawski
- Engineering and Physical Sciences Research Council