On the Non-uniqueness of Physical Scattering for Hard Non-spherical Particles

Mark Wilkinson

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


We prove the existence of uncountably-many physical scattering maps for non-spherical hard particles which, when used to construct global-in-time weak solutions of Newton’s equations of motion, conserve the total linear momentum, angular momentum and kinetic energy of the particle system for all time. We prove this result by first exhibiting the non-uniqueness of a classical solution to a constrained Monge–Ampère equation posed on Euclidean space, and then applying the deep existence theory of Ballard for hard particle dynamics. In the final section of the article, we briefly discuss the relevance of our observations to the statistical mechanics of hard particle systems.
Original languageEnglish
Pages (from-to)1-29
Number of pages29
JournalArchive for Rational Mechanics and Analysis
Early online date18 Nov 2019
Publication statusE-pub ahead of print - 18 Nov 2019

ASJC Scopus subject areas

  • Analysis
  • Mathematics (miscellaneous)
  • Mechanical Engineering


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