Local existence of weak solutions to kinetic Cucker‐Smale‐Fokker‐Planck equation with singular commutation weights-Reference-Cited by-同舟云学术

Local existence of weak solutions to kinetic Cucker‐Smale‐Fokker‐Planck equation with singular commutation weights

Published:2023-02-05 Issue:9 Volume:46 Page:9902-9921
ISSN:0170-4214
Container-title:Mathematical Methods in the Applied Sciences
language:en
Short-container-title:Math Methods in App Sciences

Author:

Li Donghao¹^ORCID,Ma Yaxian²,Zhang Xianwen³^ORCID

Affiliation:

1. College of Science Henan University of Technology Zhengzhou, Henan 450000 China

2. School of Science North University of China Taiyuan, Shanxi 030051 China

3. School of Mathematics and Statistics Huazhong University of Science and Technology Wuhan, Hubei 430074 China

Abstract

In this paper, we investigate the Cauchy problem of the dimensional kinetic Cucker‐Smale‐Fokker‐Planck equation with singular communication weight behaving like as . First, local existence of weak solutions with finite kinetic energy is established for and . Second, for , we show that any initial datum with finite velocity moment of order launches a weak solution that propagates the initial velocity moment.

Funder

National Natural Science Foundation of China

Natural Science Foundation of Henan Province

Doctoral Scientific Research Start-up Foundation from Henan University of Technology

Publisher

Wiley

Subject

General Engineering,General Mathematics

Link

https://onlinelibrary.wiley.com/doi/pdf/10.1002/mma.9092

Reference39 articles.

1. Emergent dynamics of Cucker–Smale flocking particles in a random environment

2. Discrete Cucker--Smale Flocking Model with a Weakly Singular Weight

3. On the mathematics of emergence

4. Emergent Behavior in Flocks

5. A simple proof of the Cucker-Smale flocking dynamics and mean-field limit