Macroscopic non-uniqueness and limits of Hamiltonian dynamics. (13th November 2017)

• Record Type: Journal Article
• Authors: Dostoglou, S; Xue, Jianfei
• Is Part Of: Nonlinearity. Volume 30:Number 12(2017:Dec.)
• Page Start: 4454
• Page End: 4482
• Publication Date: 2017-11-13
• Subjects: hydrodynamic equations -- Hamilton equations -- non-uniqueness; 76 -- 82C -- 28 -- 35 -- 37J -- K; Nonlinear theories -- Periodicals; Mathematical analysis -- Periodicals; Mathematical analysis; Nonlinear theories; Periodicals; 515
• DOI: 10.1088/1361-6544/aa85d7
• Languages: English
• ISSNs: 0951-7715

Abstract

Abstract: We construct explicit examples of spontaneous energy generation and non-uniqueness for the compressible Euler system, with and without pressure, by taking limits of Hamiltonian dynamics as the number of molecules increases to infinity. The examples come from rescalings of well-posed, deterministic systems of molecules that either collide elastically or interact via singular pair potentials.