Global weak solutions to the compressible Cucker–Smale–Navier–Stokes system in a bounded domain. (July 2023)

• Record Type: Journal Article
• Authors: Chen, Li; Li, Yue; Zamponi, Nicola
• Is Part Of: Nonlinear analysis. Volume 232(2023)
• Publication Date: 2023-07
• Subjects: 35Q35 -- 82C22 -- 35D30; Cucker–Smale equation -- Compressible Navier–Stokes equations -- Weak solutions -- Existence; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2023.113257
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: A coupled kinetic-fluid model is investigated, which describes the dynamic behavior of an ensemble of Cucker–Smale flocking particles interacting with a viscous fluid in a three-dimensional bounded domain. This system consists of a kinetic Cucker–Smale equation and a compressible Navier–Stokes system with nonhomogeneous boundary conditions. The global existence of weak solutions to this system with adiabatic coefficient γ > 3 / 2 is established.