On the convergence of soft potential dynamics to hard sphere dynamics

Mark Wilkinson

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

Abstract

We address a question raised in the work of Gallagher, Saint-Raymond and Texier [From Newton to Boltzmann: Hard Spheres and Short-range Potentials, European Mathematical Society (EMS), Zürich, 2013] that concerns the convergence of soft potential dynamics to hard sphere dynamics. In the case of two particles, we establish that hard sphere dynamics is the limit of soft sphere dynamics in the weak-star topology of BV. We view our result as establishing a topological method by which to construct weak solutions to the ODE of hard sphere motion.

Original languageEnglish
Pages (from-to)1-32
Number of pages32
JournalAsymptotic Analysis
Volume107
Issue number1-2
DOIs
Publication statusPublished - 9 Mar 2018

Keywords

  • Boltzmann equation
  • Hard particle dynamics
  • Hard spheres
  • Kinetic theory
  • Weak solutions

ASJC Scopus subject areas

  • Mathematics(all)

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