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

2024/02/11 by Nilasis Chaudhuri, Chaudhuri, Nilasis, Young-Pil Choi +5 · 2 citations
Earth and Planetary Sciences · Medicine · #Analysis of PDEs (math.AP) #Aquatic and Environmental Studies #Arctic and Antarctic ice dynamics #FOS: Mathematics #Mathematical and Theoretical Epidemiology and Ecology Models

paper · pdf · doi:10.48550/arxiv.2402.07130

openalex publication_date 2024/02/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Cited by

• Existence and weak-strong uniqueness of measure solutions to Euler-alignment/Aw--Rascle--Zhang model of collective behaviour
• Exponential and algebraic decay in Euler--alignment system with nonlocal interaction forces

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