Skip to main content
SpringerLink
Log in

Global Solution to the Relativistic Enskog Equation with Near-Vacuum Data

  • Published:
Journal of Statistical Physics Aims and scope Submit manuscript

Abstract

We give two hypotheses of the relativistic collision kernal and show the existence and uniqueness of the global mild solution to the relativistic Enskog equation with the initial data near the vacuum for a hard sphere gas.

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. H. Andreasson, S. Calogero and R. Illner, On blowup for gain-term-only classical and relativistic Boltzmann equations. Math. Meth. Appl. Sci. 27:2231–2240 (2004).

    Article  MATH  MathSciNet  Google Scholar 

  2. L. Arkeryd, On the Enskog equation with large initial data. SIAM J. Math. Anal. 21:631–646 (1990).

    Article  MATH  MathSciNet  Google Scholar 

  3. K. Bichteler, On the Cauchy problem of the relativistic Boltzmann equation. Commun. Math. Phys. 4:352–364 (1967).

    Article  ADS  MathSciNet  Google Scholar 

  4. S. R. de Groot, W. A. Van Leeuwen and Ch. G. Van Weert, Relativistic Kinetic Theory (North-Holland, Amsterdam, 1980).

    Google Scholar 

  5. R. J. DiPerna and P. L. Lions, On the Cauchy problem for Boltzmann equations: Global existence and weak stability. Ann. Math. 130:321 (1989).

    Article  MathSciNet  Google Scholar 

  6. M. Dudyński and M. L. Ekiel-Jeżewska, On the linearized relativistic Boltzmann equation. Commun. Math. Phys. 115:607–629 (1988).

    Article  MATH  ADS  Google Scholar 

  7. M. Dudyński and M. L. Ekiel-Jeżewska, Global existence proof for relativistic Boltzmann equation. J. Stat. Phys. 66(3/4) (1992).

  8. D. Enskog, Kinetiche Theorie der Wàrmeleitung, Reibung und Selbstdiffusion in gewissen werdichteten Gasen und Flubigkeiten. Kungl. Sv. Vetenskapsakademiens Handl. 63:3–44 (1922), English Transl. in Brush, S. G., Kinetic Theory, vol 3 (Pergamon, New York, 1972).

    Google Scholar 

  9. R. Glassey, Global solutions to the Cauchy problem for the relativistic Boltzmann equation with near-vacuum data. Comm. Math. Phys. 26:705–724 (2006).

    Article  ADS  MathSciNet  Google Scholar 

  10. R. Glassey and W. Strauss, On the derivatives of the collision map of relativistic particles. Transp. Theory Stat. Phys. 20:55–68 (1991).

    MATH  MathSciNet  Google Scholar 

  11. R. Glassey and W. Strauss, Asymptotic stability of the relativistic Maxwellian via fourteen moments. Transp. Theory Stat. Phys. 24:657–678 (1995).

    MATH  MathSciNet  Google Scholar 

  12. R. Galeano, O. Vasquez and B. Orozco, The relativistic Enskog equation. J. Differ. Equ. Conf. 13:21–27 (2005).

    Google Scholar 

  13. R. Illner and M. Shinbrot, The Boltzmann equation, global existence for a rare gas in an infinite vacuum. Comm. Math. Phys. 95:217–226 (1984).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  14. J. Polewczak, Global existence and asymptotic behavior for the nonlinear Enskog equation. SIAM J. Appl. Math. 49:952–959 (1989).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  15. S. Ukai, Solutions of the Boltzmann equation. Stud. Math. Appl. 18:37–96 (1986).

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Zhongshan University, Guangzhou, 510275, P. R. China

    Zhenglu Jiang

Authors
  1. Zhenglu Jiang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Zhenglu Jiang.

Additional information

2000 Mathematics Subject Classification. 76P05; 35Q75; 82-02.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Jiang, Z. Global Solution to the Relativistic Enskog Equation with Near-Vacuum Data. J Stat Phys 127, 805–812 (2007). https://doi.org/10.1007/s10955-006-9269-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10955-006-9269-6

Keywords

Search

Navigation