Skip to main content
SpringerLink
Log in

Classical Solutions to the Boltzmann Equation for Molecules with an Angular Cutoff

  • Published:
Archive for Rational Mechanics and Analysis Aims and scope Submit manuscript

Abstract

An important class of collision kernels in the Boltzmann theory are governed by the inverse power law, in which the intermolecular potential between two particles is an inverse power of their distance. Under the Grad angular cutoff assumption, global-in-time classical solutions near Maxwellians are constructed in a periodic box for all soft potentials with −3<γ<0.

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. Alexandre, R., Desvillettes, L., Villani, C., Wennberg, B.: Entropy dissipation and long-range interactions. Arch. Rational Mech. Anal. 152, 327–355 (2000)

    MathSciNet  MATH  Google Scholar 

  2. Alexandre, R., Villani, C.: On the Boltzmann equation for long-range interactions. Comm. Pure Appl. Math. 55, 30–70 (2002)

    MathSciNet  MATH  Google Scholar 

  3. Caflisch, R., The Boltzmann equation with a soft potential (I). Comm. Math. Phys. 74, 71–109 (1980)

    Google Scholar 

  4. Caflisch, R.: The Boltzmann equation with a soft potential (II). Comm. Math. Phys. 74, 97–109 (1980)

    MathSciNet  MATH  Google Scholar 

  5. Cercignani, C.: The Boltzmann Equation and Its Application. Springer-Verlag, 1988

  6. Cercignani, C., Illner, R., Pulvirenti, M.: The Mathematical Theory of Dilute Gases. Springer-Verlag, 1994

  7. Diperna, R., Lions, P-L.: Global weak solution of Vlasov-Maxwell systems. Comm. Pure Appl. Math. 42, 729–757 (1989)

    MathSciNet  MATH  Google Scholar 

  8. Glassey, R.: The Cauchy Problems in Kinetic Theory, SIAM, 1996

  9. Golse, F., Poupaud, F.: Stationary solutions of the linearized Boltzmann equation in a half-space. Math. Methods Appl. Sci. 11, 483–502 (1989)

    MathSciNet  MATH  Google Scholar 

  10. Goudon, T.: On the Boltzmann equation and its relations to the Landau-Fokker-Planck equation: influence of grazing collisions. C. R. Acad. Sci. Paris. Sér. I Math. 324, 265–270 (1997)

    MathSciNet  MATH  Google Scholar 

  11. Guo, Y.: The Vlasov-Poisson-Boltzmann system near Maxwellians. Comm. Pure Appl. Math. 55, 1104–1135 (2002)

    MathSciNet  MATH  Google Scholar 

  12. Guo, Y.: The Landau equation in a periodic box. Commun. Math. Phys. 231, 391–434 (2002)

    MATH  Google Scholar 

  13. Guo, Y.: The Vlasov-Maxwell-Boltzmann system near Maxwellians. Invent. Math., in press (2003)

  14. Ukai, S., Asano, K.: On the Cauchy problem of the Boltzmann equation with a soft potential. Publ. Res. Inst. Math. Sci. 18, 303–324 (1982)

    Google Scholar 

  15. Villani, C.: On a new class of weak solutions to the spatially homogeneous Boltzmann and Landau equations. Arch. Rational. Mech. Anal. 143, 273–307 (1998)

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Division of Applied Mathematics, Brown University, Providence, U.S.A

    Yan Guo

Authors
  1. Yan Guo
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yan Guo.

Additional information

Communicated by C. M. Dafermos

Rights and permissions

Reprints and permissions

About this article

Cite this article

Guo, Y. Classical Solutions to the Boltzmann Equation for Molecules with an Angular Cutoff. Arch. Rational Mech. Anal. 169, 305–353 (2003). https://doi.org/10.1007/s00205-003-0262-9

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00205-003-0262-9

Keywords

Search

Navigation