THE KINETIC CUCKER-SMALE MODEL: WELL-POSEDNESS AND ASYMPTOTIC BEHAVIOR

被引：15
|
作者：
Chen, Zili [1 ]
Yin, Xiuxia [1 ]
机构：
[1] Nanchang Univ, Sch Sci, Dept Math, Nanchang 330031, Jiangxi, Peoples R China
来源：
SIAM JOURNAL ON MATHEMATICAL ANALYSIS | 2019年 / 51卷 / 05期
基金：
中国国家自然科学基金;
关键词：
Cucker-Smale model; asymptotic behavior; velocity-spatial moment; velocity-spatial support; VLASOV-POISSON SYSTEM; GLOBAL EXISTENCE; FLOCKING DYNAMICS; WEAK SOLUTIONS; TIME DECAY; MOMENTS; PROPAGATION; REGULARITY; EQUATION; LIMIT;
D O I：
10.1137/18M1215001
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We consider well-posedness and asymptotic behavior of solutions to the kinetic Cucker-Smale model. Based on a new Lyapunov functional, we establish the global existence and uniqueness of classical solutions as well as measure-valued solutions if the initial data have compact velocity-spatial support. We also get a global weak solution if the initial datum has a bounded velocity-spatial moment of order 1. Moreover, some velocity-spatial moments decay for these solutions.
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页码：3819 / 3853
页数：35
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