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2026 / September Volume 21 No.3
Emergent dynamics of passive particles driven by self-consistent nonlocal Burgers' field
Published Date
2026 / September
Title
Emergent dynamics of passive particles driven by self-consistent nonlocal Burgers' field
Author
Seung-Yeal Ha, Xiongtao Zhang
Keyword
Cucker-Smale model, Burgers equation, velocity alignment
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Pagination
275-309
Abstract

We study the large-time dynamics of passive particles driven by Burgers' flow field. Our governing system consists of the continuity equation for passive particles and Burgers' flow field with non-local Cucker-Smale type velocity alignment. For the proposed coupled system, when initial data are sufficiently regular and small, we show that a global classical solution exists and it exhibits an asymptotic flocking phenomenon. In particular, we remove the non-vacuum assumption set up in [23] and our main result holds for any dimension.

DOI
10.21915/BIMAS.2026301
https://doi.org/10.21915/BIMAS.2026301
AMS Subject
Classification
35A09, 35B40, 35Q70
Received
2025-07-29
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