Macroscopic Non-uniqueness and Limits of Hamiltonian Dynamics

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 s...

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Bibliographic Details
Published inarXiv.org
Main Authors Dostoglou, Stamatis, Xue, Jianfei
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 28.09.2016
Subjects
Compressibility
Quantum theory
Structural adjustment
Uniqueness
Well posed problems
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Summary: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.
ISSN:2331-8422