Coupled Self-Organized Hydrodynamics and Navier-Stokes models: local well-posedness and the limit from the Self-Organized Kinetic-fluid models

Abstract

A coupled system of self-organized hydrodynamics and Navier-Stokes equations (SOH-NS), which models self-propelled particles in a viscous fluid, was recently derived by Degond et al. \cite{DMVY-2017-arXiv}, starting from a micro-macro particle system of Vicsek-Navier-Stokes model, through an intermediate step of a self-organized kinetic-kinetic model by multiple coarse-graining processes. We first transfer SOH-NS into a non-singular system by stereographic projection, then prove the local in time well-posedness of classical solutions by energy method. Furthermore, employing the Hilbert expansion approach, we justify the hydrodynamic limit from the self-organized kinetic-fluid model to macroscopic dynamics. This provides the first analytically rigorous justification of the modeling and asymptotic analysis in \cite{DMVY-2017-arXiv}.

42 pages. arXiv admin note: text overlap with arXiv:1706.05666 by other authors

References in corpus (2)

• Novel type of phase transition in a system of self-driven particles
• Coupled Self-Organized Hydrodynamics and Stokes models for suspensions of active particles

Cited by in corpus (2)

• From Kinetic Flocking Model of Cucker-Smale Type to Self-Organized Hydrodynamic model
• Cauchy theory for general Vicsek models in collective dynamics and mean-field limit approximations