Skip to main content
SpringerLink
Log in

New a priori estimates for the spatially homogeneous Boltzmann equation

  • Published:
Continuum Mechanics and Thermodynamics Aims and scope Submit manuscript

Abstract

Given the solutionf(t) to the spatially homogeneous Boltzmann equation, we study the time evolution of the Linnik's functionalJ(f(t)).

When the Boltzmann equation for Maxwellian pseudomolecules with planar velocities is considered, it is proven thatJ(f(t)) is decreasing in time.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Cercignani, C.: Theory and application of the Boltzmann equation Springer-Verlag New York (1988)

    Google Scholar 

  2. Truesdell, C.; Muncaster, R. G.: Fundamentals of Maxwell's kinetic theory of a simple monoatomic gas Academic Press, New York (1980)

    Google Scholar 

  3. Linnik, Y. V.: An information-theoretic proof of the central limit theorem with the Lindeberg condition. Theory Probab. Appl.4 (1959) 288–299

    Google Scholar 

  4. McKean Jr., H. P.: Speed of approach to equilibrium for Kac's caricature of a Maxwellian gas. Arch. Rat. Mech. Anal.21 (1966) 343–367

    Google Scholar 

  5. Toscani, G.: Strong convergence towards equilibrium for a gas of Maxwellian pseudomolecules. Continuum Mech. Thermodyn.4 (1992) 95–107

    Google Scholar 

  6. Bobylev, A. V.: The theory of the nonlinear spatially uniform Boltzmann equation for Maxwell molecules. Soviet Scient. Rev. C,7 (1988) 111–233

    Google Scholar 

  7. Bellomo, N.; Palczewski, A.; Toscani, G.: Mathematical topics in nonlinear kinetic theory. World Scientific Singapore (1988)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dipartimento di Matematica, Università di Ferrara, Ferrara, Italy

    G. Toscani

Authors
  1. G. Toscani
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Toscani, G. New a priori estimates for the spatially homogeneous Boltzmann equation. Continuum Mech. Thermodyn 4, 81–93 (1992). https://doi.org/10.1007/BF01125691

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01125691

Keywords

Search

Navigation