Discrete Cucker-Smale Flocking Model with a Weakly Singular Weight

For the discrete Cucker-Smale's flocking model with a singular communication weight $\psi(s) = s^{-\alpha}$, with $0<\alpha<1/2$ , we prove that the velocity component of certain type of weak solutions is absolutly continuous. This result enables us to obtain existence and uniqeness of global solutions.

[1]  Jos'e A. Carrillo,et al.  A well-posedness theory in measures for some kinetic models of collective motion , 2009, 0907.3901.

[2]  Jan Peszek,et al.  Existence of piecewise weak solutions of a discrete Cucker-Smale's flocking model with a singular communication weight , 2013, 1302.4224.

[3]  J. A. Carrillo,et al.  The derivation of swarming models: Mean-field limit and Wasserstein distances , 2013, 1304.5776.

[4]  Eitan Tadmor,et al.  A New Model for Self-organized Dynamics and Its Flocking Behavior , 2011, 1102.5575.

[5]  Jesús Rosado,et al.  Asymptotic Flocking Dynamics for the Kinetic Cucker-Smale Model , 2010, SIAM J. Math. Anal..

[6]  F. Cucker,et al.  Flocking in noisy environments , 2007, 0706.3343.

[7]  Axel Klar,et al.  SELF-PROPELLED INTERACTING PARTICLE SYSTEMS WITH ROOSTING FORCE , 2010 .

[8]  Seung-Yeal Ha,et al.  EMERGENCE OF MULTI-CLUSTER CONFIGURATIONS FROM ATTRACTIVE AND REPULSIVE INTERACTIONS , 2012 .

[9]  Seung-Yeal Ha,et al.  On collision-avoiding initial configurations to Cucker-Smale type flocking models , 2012 .

[10]  Seung-Yeal Ha,et al.  Fast-slow dynamics of planar particle models for flocking and swarming , 2012 .

[11]  Seung-Yeal Ha,et al.  A CLASS OF INTERACTING PARTICLE SYSTEMS ON THE INFINITE CYLINDER WITH FLOCKING PHENOMENA , 2012 .

[12]  J. Peszek,et al.  On certain generalizations of the Gagliardo–Nirenberg inequality and their applications to capacitary estimates and isoperimetric inequalities , 2013 .

[13]  Vicsek,et al.  Novel type of phase transition in a system of self-driven particles. , 1995, Physical review letters.

[14]  Felipe Cucker,et al.  Avoiding Collisions in Flocks , 2010, IEEE Transactions on Automatic Control.

[15]  Pierre Degond,et al.  Macroscopic limit of self-driven particles with orientation interaction , 2007 .

[16]  F. Cucker,et al.  Flocking with informed agents , 2008 .

[17]  Andrea L. Bertozzi,et al.  Swarming Patterns in a Two-Dimensional Kinematic Model for Biological Groups , 2004, SIAM J. Appl. Math..

[18]  Pierre Degond,et al.  Continuum limit of self-driven particles with orientation interaction , 2007, 0710.0293.

[19]  E. Tadmor,et al.  From particle to kinetic and hydrodynamic descriptions of flocking , 2008, 0806.2182.

[20]  J. Carrillo,et al.  Local well-posedness of the generalized Cucker-Smale model , 2014, 1406.1792.

[21]  P. Degond,et al.  Large Scale Dynamics of the Persistent Turning Walker Model of Fish Behavior , 2007, 0710.4996.

[22]  Massimo Fornasier,et al.  A Kinetic Flocking Model with Diffusion , 2010 .

[23]  Seung-Yeal Ha,et al.  Stochastic flocking dynamics of the Cucker–Smale model with multiplicative white noises , 2010 .

[24]  H. Jin Kim,et al.  Cucker-Smale Flocking With Inter-Particle Bonding Forces , 2010, IEEE Transactions on Automatic Control.

[25]  Jan Peszek,et al.  On some nonlinear extensions of the Gagliardo-Nirenberg inequality with applications to nonlinear eigenvalue problems , 2011, Asymptot. Anal..

[26]  Felipe Cucker,et al.  Emergent Behavior in Flocks , 2007, IEEE Transactions on Automatic Control.

[27]  Seung-Yeal Ha,et al.  A simple proof of the Cucker-Smale flocking dynamics and mean-field limit , 2009 .

[28]  Seung-Yeal Ha,et al.  Flocking and synchronization of particle models , 2010 .

[29]  Seung-Yeal Ha,et al.  Emergence of time-asymptotic flocking in a stochastic Cucker-Smale system , 2009 .

[30]  Jianhong Shen,et al.  Cucker–Smale Flocking under Hierarchical Leadership , 2006, q-bio/0610048.

[31]  Seung-Yeal Ha,et al.  Asymptotic dynamics for the Cucker–Smale-type model with the Rayleigh friction , 2010 .

[32]  M. Slemrod,et al.  Flocking Dynamics of Singularly Perturbed Oscillator Chain and the Cucker-Smale System , 2010 .

[33]  W. Marsden.  I and J , 2012 .