Bulletin des Sciences Mathématiques· 2026Q1
Conservative formulations of the Standard Enskog and Povzner equations
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- 2026year
Short summary
This paper presents a conservative formulation of the Standard Enskog and Povzner equations, showing their collision integrals can be expressed as velocity-dependent mass current divergences.
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Key points
- Introduces conservative formulations for Standard Enskog and Povzner equations.
- Expresses collision integrals as divergence of mass current w.r.t. velocity.
- Represents v C[f,f] and |v|^2 C[f,f] as phase-space divergences.
- Extends Villani's result for Boltzmann equation to dense gases.
AI-generated from the title and abstract; the full text is not read.
Abstract
This article introduces a conservative formulation of the Standard Enskog equation and the Povzner equation, both of which generalize the Boltzmann equation by incorporating the contribution of particle volume in collisions. The primary result expresses these collision integrals as the divergence with respect to the velocity variable v of a mass current. Moreover, the terms v C[f,f] and |v|^2 C[f,f], where C[f,f] denotes the Standard Enskog or Povzner collision integral, are represented as phase-space divergences (that is, divergences in both position and velocity) of corresponding momentum and energy currents. This work extends Villani's earlier result (Math. Modelling Numer. Anal. M2AN 33 (1999), 209--227) for the classical Boltzmann equation to the case of dense gases.
The authors' abstract, as published at the source. Bulletin des Sciences Mathématiques, 2026 · DOI ↗
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Field: Mechanics of Materials
Mechanics of MaterialsEngineering