About the Use of Entropy Production for the Landau-Fermi-Dirac Equation

被引：8

作者：

Alonso, R. ^{[1
,2
]}

Bagland, V. ^{[3
]}

Desvillettes, L. ^{[4
,5
]}

Lods, B. ^{[6
,7
]}

机构：

[1] Texas A&M Univ Qatar, Dept Sci, Doha, Qatar

[2] Pontificia Univ Catolica Rio de Janeiro, Dept Matemat, Rio de Janeiro, Brazil

[3] Univ Clermont Auvergne, LMBP, UMR CNRS 6620, Campus Cezeaux,3,Pl Vasarely,TSA 60026,CS 60026, F-63178 Aubiere, France

[4] Univ Paris, Inst Math Jussieu Paris Rive Gauche, F-75013 Paris, France

[5] Sorbonne Univ, CNRS, F-75013 Paris, France

[6] Univ Torino, Dept Econ Social Sci Appl Math & Stat ESOMAS, Corso Unione Soviet,218 Bis, I-10134 Turin, Italy

[7] Univ Torino, Coll Carlo Alberto, Corso Unione Soviet,218 Bis, I-10134 Turin, Italy

来源：

JOURNAL OF STATISTICAL PHYSICS | 2021年 / 183卷 / 01期

关键词：

Landau– Fermi– Dirac equation; Landau equation; Quantum kinetic models; Entropy; Fisher Information;

D O I：

10.1007/s10955-021-02751-z

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

In this paper, we present new estimates for the entropy dissipation of the Landau-Fermi-Dirac equation (with hard or moderately soft potentials) in terms of a weighted relative Fisher information adapted to this equation. Such estimates are used for studying the large time behaviour of the equation, as well as for providing new a priori estimates (in the soft potential case). An important feature of such estimates is that they are uniform with respect to the quantum parameter. Consequently, the same estimations are recovered for the classical limit, that is the Landau equation.

引用

页数：27

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