Well posedness for pressureless Euler system with a flocking dissipation in Wasserstein space. (November 2015)

• Record Type: Journal Article
• Authors: Jin, Chunyin
• Is Part Of: Nonlinear analysis. Volume 128(2015)
• Page Start: 412
• Page End: 422
• Publication Date: 2015-11
• Subjects: Pressureless Euler system -- Cucker–Smale model -- Conservation law -- Flocking; 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.2015.08.003
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We prove the well posedness of nonhomogeneous pressureless Euler system in 2-Wasserstein space with the initial mass and energy being finite. Our method is based on a main observation pioneered by Brenier and Grenier that we can recover the solution of the pressureless system from a conservation law with its flux function being determined by the initial density and velocity.