Skip to main content
SpringerLink
Log in

The Development of the Green's Function for the Boltzmann Equation

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

Abstract

We review the particle-like and wave-like property of the Boltzmann equation. This property leads to a sequence of developments on the mathematical theory of the Green's function for the Boltzmann equation.

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. C. Cercignani, The Boltzmann Equation and Its Applications (Springer Verlag, Berlin, 1988).

    MATH  Google Scholar 

  2. C. Cercignani, R. Illner, and M. Pulvirenti, The mathematical theory of dilute gases, Applied Mathematical Sciences Vol. 106 (Springer-Verlag, New York, 1994).

  3. R. Ellis and R. M. Pinsky, The first and second fluid approximations to the linearized Boltzmann equation, J. Math. Pures Appl. 54(9):125–156 (1975).

    MATH  MathSciNet  Google Scholar 

  4. D. Hilbert, Grundzüge einer Allgemeinen Theorie der Linearen Integralgleichungen (Teubner, Leipzig, 1912).

  5. T.-P. Liu and S.-H. Yu, The Green's function and large-time behavior of solutions for the one-dimensional Boltzmann equation, Comm. Pure Appl. Math. 57(12):1543–1608 (2004).

    Article  MATH  MathSciNet  Google Scholar 

  6. T.-P. Liu and S.-H. Yu, Green's Function and Large-Time behavior of Solutions of Boltzmann Equation, 3-D Waves, to appear.

  7. T.-P. Liu and S.-H. Yu, Initial-boundary value problem for boltzmann equation, planar waves, to appear

  8. T.-P. Liu and W. Wang, The pointwise estimates of diffusion wave for the Navier–Stokes systems in odd multi-dimensions, Comm. Math. Phys. 196(1):145–173 (1998).

    Article  MATH  MathSciNet  ADS  Google Scholar 

  9. T.-P. Liu and Y. Zeng, Large time behavior of solutions for general quasilinear hyperbolic-parabolic systems of conservation laws, Mem. Amer. Math. Soc. 125(599) (1997).

  10. Y. Sone, Kinetic Theory and Fluid Dynamics (Birkhauser, 2002).

  11. S. Ukai, Les solutions globales de l'équation de Boltzmann dans l'espace tout entier et dans le demi-espace, C. R. Acad. Sci. Paris Ser. A-B 282(6):Ai, A317–A320 (1976).

  12. S. Ukai, T. Yang, and S.-H. Yu, Nonlinear boundary layers of the Boltzmann equation. I. Existence. Comm. Math. Phys. 236(3):373–393 (2003).

    Article  MATH  MathSciNet  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, City University of Hong Kong, Kowloon, Hong Kong, SAR, China

    Shih-Hsien Yu

Authors
  1. Shih-Hsien Yu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Shih-Hsien Yu.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Yu, SH. The Development of the Green's Function for the Boltzmann Equation. J Stat Phys 124, 301–320 (2006). https://doi.org/10.1007/s10955-006-9064-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10955-006-9064-4

Key words

Search

Navigation