| Summary: | 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 $\beta \in (0,3)$.
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