Skip to main content
Disciplines
Automotive Business IT + Informatics Construction + Real Estate Electrical Engineering + Electronics Energy + Sustainability Insurance + Risk Finance + Banking Management + Leadership Marketing + Sales Mechanical Engineering + Materials
DE
EN
Books
Journals
Events
Topic Page
Marketing
Log in
Learn more about individual access
Request company access
13th International Engine Congress 2026 | 24 + 25 February 2026

Meeting Place for the Powertrain and Sustainable Fuels Community

Take part as a speaker in the 13th International Engine Congress 2026, the Meeting Place for the Powertrain, and Sustainable Fuels Community for the exchange of experience. Submit a subject proposal online about our main subject areas: Passenger car engine technology, Commercial vehicle engine technology and Sustainable Fuels & Energy!
EXTENDED SEARCH
Log in
Top
Published in:
Read chapter Read first chapter

2024 | OriginalPaper | Chapter

Some Remarks About the Link Between the Fisher Information and Landau or Landau-Fermi-Dirac Entropy Dissipation

Author : Laurent Desvillettes

Published in: From Particle Systems to Partial Differential Equations

Publisher: Springer International Publishing

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

We present in this work variants of existing estimates for the Landau or Landau-Fermi-Dirac entropy dissipation, in terms of Fisher information, in the hard potential case. The specificity of those variants is that the entropy is never used in the estimates (in order to control possible concentrations on a zero measure set). The proofs are significantly simplified with respect to previous papers on the subject.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

inform now
previous chapter Radial Laplacian on Rotation Groups
next chapter The Entropic Journey of Kac’s Model
Literature
1.
Alonso, R., Bagland, V., Lods, B.: Long time dynamics for the Landau-Fermi-Dirac equation with hard potentials. J. Differential Equations 270, 596–663 (2021)MathSciNetCrossRef
2.
R. Alonso, V. Bagland, L. Desvillettes, and B. Lods: About the use of entropy production for the Landau-Fermi-Dirac equation. Journal of Statistical Physics 183, (2021)
3.
Alonso, R., Bagland, V., Desvillettes, L., Lods, B.: About the Landau-Fermi-Dirac equation with moderately soft potentials. Arch. Rational Mech. Anal 244, 779–875 (2022)MathSciNetCrossRef
4.
Bagland, V.: Well-posedness for the spatially homogeneous Landau-Fermi-Dirac equation for hard potentials. Proc. Roy. Soc. Edinburgh Sect. A. 134, 415–447 (2004)MathSciNetCrossRef
5.
Carrillo, J.A., Laurençot, Ph., Rosado, J.: Fermi-Dirac-Fokker-Planck equation: well-posedness and long-time asymptotics. J. Differential Equations 247, 2209–2234 (2009)MathSciNetCrossRef
6.
Carlen, E.A., Carvalho, M.C.: Strict entropy production bounds and stability of the rate of convergence to equilibrium for the Boltzmann equation. J. Stat. Phys. 67(3–4), 575–608 (1992)MathSciNetCrossRef
7.
Carlen, E.A., Carvalho, M.C.: Entropy production estimates for Boltzmann equations with physically realistic collision kernels. J. Stat. Phys. 74(3–4), 743–782 (1994)MathSciNetCrossRef
8.
Carrapatoso, K., Desvillettes, L., He, L.: Estimates for the large time behavior of the Landau equation in the Coulomb case. Arch. Rational Mech. Anal. 224, 381–420 (2017)MathSciNetCrossRef
9.
Chapman, S., Cowling, T.G.: The mathematical theory of non-uniform gases. Cambridge Univ. Press, London (1952)
10.
Desvillettes, L.: Entropy dissipation rate and convergence in kinetic equations. Commun. Math. Phys. 123(4), 687–702 (1989)MathSciNetCrossRef
11.
Desvillettes, L.: Entropy dissipation estimates for the Landau equation in the Coulomb case and applications. J. Funct. Anal. 269, 1359–1403 (2015)MathSciNetCrossRef
12.
L. Desvillettes. Entropy dissipation estimates for the Landau equation: General cross sections. Proceedings of the conference PSPDE III, Braga, 2014
13.
L. Desvillettes. Structure entropique du noyau de collision de Landau, Proceedings of the seminar Laurent Schwartz - EDP et applications (2014-2015), Exp. No. 14
14.
L. Desvillettes. About Boltzmann’s H Theorem for Landau Equation (Autour du Théorème H de Boltzmann), Proceedings of the seminar Laurent Schwartz - EDP et applications (2019-2020), Exp. No. 9
15.
L. Desvillettes, L.-B. He and J.-C. Jiang. A new monotonicity formula for the spatially homogeneous Landau equation with Coulomb potential and its applications. Preprint arXiv:​2011.​00386. Accepted for publication in the J. European Math. Society
16.
Desvillettes, L., Mouhot, C., Villani, C.: Celebrating Cercignani’s conjecture for the Boltzmann equation. Kinet. Relat. Models 4, 277–294 (2011)MathSciNetCrossRef
17.
L. Desvillettes and C. Villani. On the spatially homogeneous Landau equation for hard potentials. Part I. Existence, uniqueness and smoothness. Commun. Partial Differential Equations, 25, n.1-2 (2000), 179-259
18.
L. Desvillettes and C. Villani. On the spatially homogeneous Landau equation for hard potentials. Part II. H-Theorem and applications. Commun. Partial Differential Equations, 25, n.1-2 (2000), 261-298
19.
Golse, F., Gualdani, M.-P., Imbert, C., Vasseur, A.: Partial Regularity in Time for the Space-Homogeneous Landau equation with Coulomb Potential. Ann. Sci. Ecole Normale Supérieure 55(6), 1575–1611 (2022)MathSciNetCrossRef
20.
21.
Lifschitz, E.M., Pitaevskii, L.P.: Physical kinetics. Perg. Press, Oxford (1981)
22.
Lu, X., Wennberg, B.: On stability and strong convergence for the spatially homogeneous Boltzmann equation for Fermi-Dirac particles. Arch. Ration. Mech. Anal. 168, 1–34 (2003)MathSciNetCrossRef
23.
Toscani, G.: Entropy production and the rate of convergence to equilibrium for the Fokker-Planck equation. Quart. Appl. Math. 57(3), 521–541 (1999)MathSciNetCrossRef
24.
Toscani, G., Villani, C.: On the trend to equilibrium for some dissipative systems with slowly increasing a priori bounds. J. Statist. Phys. 98(5–6), 1279–1309 (2000)MathSciNetCrossRef
25.
Wu, K.-C.: Global in time estimates for the spatially homogeneous Landau equation with soft potentials. J. Funct. Anal. 266, 3134–3155 (2014)MathSciNetCrossRef
Metadata
Title
Some Remarks About the Link Between the Fisher Information and Landau or Landau-Fermi-Dirac Entropy Dissipation
Author
Laurent Desvillettes
Copyright Year
2024
Book
From Particle Systems to Partial Differential Equations

Print ISBN: 978-3-031-65194-6

Electronic ISBN: 978-3-031-65195-3

Copyright Year: 2024

DOI
https://doi.org/10.1007/978-3-031-65195-3_3

Premium Partner

    Image Credits