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Pré-Publication, Document De Travail Année : 2014

Local well-posedness of the generalized Cucker-Smale model

Résumé

In this paper, we study the local well-posedness of two types of generalized Cucker-Smale (in short C-S) flocking models. We consider two different communication weights, singular and regular ones, with nonlinear coupling velocities $v|v|^{\beta-2}$ for $\beta > \frac{3-d}{2}$. For the singular communication weight, we choose $\psi^1(x) = 1/|x|^{\alpha}$ with $\alpha \in (0,d-1)$ and $\beta \geq 2$ in dimension $d > 1$. For the regular case, we select $\psi^2(x) \geq 0$ belonging to $(L_{loc}^\infty \cap \mbox{Lip}_{loc})(\mathbb{R}^d)$ and $\beta \in (\frac{3-d}{2},2)$. We also remark the various dynamics of C-S particle system for these communication weights when $\beta \in (0,3)$.

Dates et versions

hal-01257033 , version 1 (15-01-2016)

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J. A. Carrillo, Y. -P. Choi, Maxime Hauray. Local well-posedness of the generalized Cucker-Smale model. 2014. ⟨hal-01257033⟩
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