Work

Fisher information for solutions of the Boltzmann equation

Year: 2026

Type: article

Abstract: This note reviews a recent contribution about the Fisher information for the space-homogeneous Boltzmann equation by L. Silvestre, C. Villani and the author ( arXiv, 2024 ). This classical functional from information theory is shown to be non-increasing along the flow of the non-linear PDE for all physically relevant particle interactions. The proof consists in establishing a new functional inequality on the sphere of Log-Sobolev type. This new a priori estimate on solutions yields global-in-time well posedness of the equation, in particular in the case of very singular interactions, a left open question up to this work.

Source: Journées Équations aux dérivées partielles

DOI: 10.5802/jedp.693

Author: Cyril Imbert

Institutions: Centre National de la Recherche Scientifique, Université Paris Sciences et Lettres, École Normale Supérieure - PSL, Département de mathématiques et applications

Language: English

Topic: Gas Dynamics and Kinetic Theory

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

OpenAlex ID: W4417410268

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