Coupled Self-organized Hydrodynamics and Navier–Stokes Models : Local Well-posedness and the Limit from the Self-organized Kinetic-Fluid Models

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journal

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Author(s)

  • Ning JIANG
  • Yi-Long LUO
  • Teng-Fei ZHANG

Related Research Unit(s)

Detail(s)

Original languageEnglish
Pages (from-to)329–387
Journal / PublicationArchive for Rational Mechanics and Analysis
Volume236
Issue number1
Online published3 Dec 2019
Publication statusPublished - Apr 2020

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. (J Math Fluid Mech 21(1), Art. 6, 36, 2019), starting from a micro-macro particle system of Vicsek–Navier–Stokes model, through an intermediate step of a self-organized kinetic-fluid model by multiple coarse-graining processes. In spherical coordinates, the SOH-NS system is singular. To avoid this coordinate singularity, 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, by employing the Generalized Collision Invariants (GCI)-based Hilbert expansion approach, we justify the hydrodynamic limit from the self-organized kinetic-fluid model to macroscopic dynamics with optimal convergence rate. This provides the first analytically rigorous justification of the modeling and asymptotic analysis in Degond et al. (2019).

Research Area(s)

  • BOLTZMANN-EQUATION, PHASE-TRANSITION, DIFFUSIVE LIMIT, ACOUSTIC LIMIT, EXISTENCE, PARTICLES, DYNAMICS, SYSTEM, LEVEL

Citation Format(s)

Coupled Self-organized Hydrodynamics and Navier–Stokes Models : Local Well-posedness and the Limit from the Self-organized Kinetic-Fluid Models. / JIANG, Ning; LUO, Yi-Long; ZHANG, Teng-Fei.

In: Archive for Rational Mechanics and Analysis, Vol. 236, No. 1, 04.2020, p. 329–387.

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journal