Recent Issues
Volume 14, Issue 2
Volume 14, Issue 1
Volume 13, Issue 4
Volume 13, Issue 3
Volume 13, Issue 2
Volume 13, Issue 1
Volume 12, Issue 4
Volume 12, Issue 3
Volume 12, Issue 2
Volume 12, Issue 1
Volume 11, Issue 4
Volume 11, Issue 3
Volume 11, Issue 2
Volume 11, Issue 1
Volume 10, Issue 4
Volume 10, Issue 3
Volume 10, Issue 2
Volume 10, Issue 1
Volume 9, Issue 4
Volume 9, Issue 3
Volume 9, Issue 2
Volume 9, Issue 1
Volume 8, Issue 4
Volume 8, Issue 3
Volume 8, Issue 2
Volume 8, Issue 1
Volume 7, Issue 4
Volume 7, Issue 3
Volume 7, Issue 2
Volume 7, Issue 1
Volume 6, Issue 4
Volume 6, Issue 3
Volume 6, Issue 2
Volume 6, Issue 1
Volume 5, Issue 3-4
Volume 5, Issue 2
Volume 5, Issue 1
Volume 4, Issue 3-4
Volume 4, Issue 2
Volume 4, Issue 1
Volume 3, Issue 4
Volume 3, Issue 3
Volume 3, Issue 2
Volume 3, Issue 1
Volume 2, Issue 2
Volume 2, Issue 1
Volume 1, Issue 2
Volume 1, Issue 1
Abstract
We review and compare mathematical procedures aimed at rigorously deriving
fluid-dynamic descriptions of classical particle systems in the large-scale limit of
Hamiltonian dynamics. Despite the longstanding nature of this program, its
fundamental problems remain open, with only a few notable exceptions that we
briefly highlight.
Keywords
hydrodynamical limit, microscopic derivation, large scale
limit, Euler equation, Boltzmann equation
Mathematical Subject Classification
Primary: 82-02
Milestones
Received: 20 November 2025
Accepted: 7 December 2025
Published: 27 December 2025
Communicated by Francesco dell'Isola
© 2026 MSP (Mathematical Sciences
Publishers).
