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Title: On the structure of limiting flocks in hydrodynamic Euler Alignment models
The goal of this paper is to study limiting behavior of a self-organized continuous flock evolving according to the 1D hydrodynamic Euler Alignment model. We provide a series of quantitative estimates that show how far the density of the limiting flock is from a uniform distribution. The key quantity that controls density distortion is the entropy [Formula: see text], and the measure of deviation from uniformity is given by a well-known conserved quantity [Formula: see text], where [Formula: see text] is velocity and [Formula: see text] is the communication operator with kernel [Formula: see text]. The cases of Lipschitz, singular geometric, and topological kernels are covered in the study.  more » « less
Award ID(s):
1813351
PAR ID:
10358271
Author(s) / Creator(s):
;
Date Published:
Journal Name:
Mathematical Models and Methods in Applied Sciences
Volume:
29
Issue:
13
ISSN:
0218-2025
Page Range / eLocation ID:
2419 to 2431
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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