Geodesic
Local well-posedness of the generalized Cucker-Smale model with singular kernels
José A. Carrillo1 ; Young-Pil Choi1 ; Maxime Hauray2
1 Department of Mathematics, Imperial College London, London SW7 2AZ, United Kingdom,
2 Centre de Mathématiques et Informatique (CMI), Université de Provence, Technopôle Château-Gombert, Marseille, France,
ESAIM. Proceedings, Tome 47 (2014), pp. 17-35 Cet article a éte moissonné depuis la source EDP Sciences

Voir la notice de l'article

In this paper, we study the local well-posedness of two types of generalized kinetic Cucker-Smale (in short C-S) equations. We consider two different communication weights in space with nonlinear coupling of the velocities, v | v | β − 2 for β > 3-d/2, where singularities are present either in space or in velocity. For the singular communication weight in space, ψ1(x) = 1 / | x | α with α ∈ (0,d − 1), d ≥ 1, we consider smooth velocity coupling, β ≥ 2. For the regular one, we assume ψ2(x) ∈ (Lloc∞ ∩ Liploc) (Rd) but with a singular velocity coupling β ∈ (3-d/2, 2). We also present the various dynamics of the generalized C-S particle system with the communication weights ψi,i = 1,2 when β ∈ (0,3). We provide sufficient conditions of the initial data depending on the exponent β leading to finite-time alignment or to no collisions between particles in finite time.
DOI : 10.1051/proc/201447002

José A. Carrillo 1 ; Young-Pil Choi 1 ; Maxime Hauray 2

1 Department of Mathematics, Imperial College London, London SW7 2AZ, United Kingdom,
2 Centre de Mathématiques et Informatique (CMI), Université de Provence, Technopôle Château-Gombert, Marseille, France, 
@article{EP_2014_47_a2,
     author = {Jos\'e A. Carrillo and Young-Pil Choi and Maxime Hauray},
     title = {Local well-posedness of the generalized {Cucker-Smale} model with singular kernels},
     journal = {ESAIM. Proceedings},
     pages = {17--35},
     year = {2014},
     volume = {47},
     doi = {10.1051/proc/201447002},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/proc/201447002/}
}
TY  - JOUR
AU  - José A. Carrillo
AU  - Young-Pil Choi
AU  - Maxime Hauray
TI  - Local well-posedness of the generalized Cucker-Smale model with singular kernels
JO  - ESAIM. Proceedings
PY  - 2014
SP  - 17
EP  - 35
VL  - 47
UR  - http://geodesic.mathdoc.fr/articles/10.1051/proc/201447002/
DO  - 10.1051/proc/201447002
LA  - en
ID  - EP_2014_47_a2
ER  - 
%0 Journal Article
%A José A. Carrillo
%A Young-Pil Choi
%A Maxime Hauray
%T Local well-posedness of the generalized Cucker-Smale model with singular kernels
%J ESAIM. Proceedings
%D 2014
%P 17-35
%V 47
%U http://geodesic.mathdoc.fr/articles/10.1051/proc/201447002/
%R 10.1051/proc/201447002
%G en
%F EP_2014_47_a2
José A. Carrillo; Young-Pil Choi; Maxime Hauray. Local well-posedness of the generalized Cucker-Smale model with singular kernels. ESAIM. Proceedings, Tome 47 (2014), pp. 17-35. doi: 10.1051/proc/201447002

Cité par Sources :