On Hydrodynamic Equations at the Limit of Infinitely Many Molecules

We show that weak convergence of point measures and \((2+\epsilon)\)-moment conditions imply hydrodynamic equations at the limit of infinitely many interacting molecules. The conditions are satisfied whenever the solutions of the classical equations for \(N\) interacting molecules obey uniform in \(...

Full description

Saved in:
Bibliographic Details
Published inarXiv.org
Main Authors Dostoglou, Stamatis, Jacob, Nicholas, Xue, Jianfei
Format Paper Journal Article
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 06.06.2014
Subjects
Hydrodynamic equations
Initial conditions
Macroscopic equations
Mathematical analysis
Mathematics - Mathematical Physics
Physics - Mathematical Physics
Rescaling
Online AccessGet full text

Cover

More Information
Summary:We show that weak convergence of point measures and \((2+\epsilon)\)-moment conditions imply hydrodynamic equations at the limit of infinitely many interacting molecules. The conditions are satisfied whenever the solutions of the classical equations for \(N\) interacting molecules obey uniform in \(N\) bounds. As an example, we show that this holds when the initial conditions are bounded and that the molecule interaction, a certain \(N\)-rescaling of potentials that include all \(r^{-p}\) for \(1<p\), is weak enough at the initial time. In this case the hydrodynamic equations coincide with the macroscopic equations of Maxwell.
ISSN:2331-8422
DOI:10.48550/arxiv.1406.1816