Why do solutions of the Maxwell-Boltzmann equation tend to be Gaussians? A simple answer
type: Item
instance of: scholarly article
title: Why do solutions of the Maxwell-Boltzmann equation tend to be Gaussians? A simple answer
zbMATH Open document ID: 1377.39035
author: Dirk Hundertmark
author: Young-Ran Lee
published in: Documenta Mathematica
publication date: 2017-11-21T00:00:00Z
review text: Summary: The Maxwell-Boltzmann functional equation has recently attraction renewed interest since besides its importance in Boltzmann's kinetic theory of gases it also characterizes maximizers of certain bilinear estimates for solutions of the free Schrödinger equation. In this note we give a short and simple proof that, under some mild growth restrictions, any measurable complex-valued solution of the Maxwell-Boltzmann equation is a Gaussian. This covers most, if not all, of the applications.
Mathematics Subject Classification ID: 39B32
Mathematics Subject Classification ID: 82C40
zbMATH DE Number: 6810411
zbMATH Keywords: Maxwell-Boltzmann functional equation
zbMATH Keywords: Gaussian maximizers
zbMATH Keywords: kinetic theory of gases
zbMATH Keywords: Schrödinger equation
zbMATH Keywords: measurable complex-valued solution
MaRDI profile type: Publication
cites work: On a functional equation arising in the kinetic theory of gases
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DOI: 10.25537/DM.2017V22.1267-1273
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description: scientific article; zbMATH DE number 6810411