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Some considerations on the fluid-dynamical limit of particle systems

Mario Pulvirenti and Sergio Simonella
Vol. 14 (2026), No. 2, 143–154
DOI: 10.2140/memocs.2026.14.143
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.

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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
Authors
Mario Pulvirenti
Dipartimento di Matematica
Sapienza Università di Roma
Rome
Italy
Sergio Simonella
Dipartimento di Matematica
Sapienza Università di Roma
Roma
Italy
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