Work

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

Year: 2025

Type: article

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.

Source: Journal of the London Mathematical Society

DOI: 10.1112/jlms.70088

Authors: Nilasis Chaudhuri, Young‐Pil Choi, Oliver Tse, Ewelina Zatorska

Institutions: University of Warsaw, Yonsei University, Eindhoven University of Technology, University of Warwick

Language: English

Topic: Navier-Stokes equation solutions

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green