Skip to main content

Perturbations of Equilibria

  • Chapter
Slow Rarefied Flows

Part of the book series: Progress in Mathematical Physics ((PMP,volume 41))

  • 628 Accesses

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 109.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 139.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. A. A. Arsen’ev, The Cauchy problem for the linearized Boltzmann equation, USSR Comput. Math. and Math. Phys. 5, 110–136 (1965)

    Article  MathSciNet  MATH  Google Scholar 

  2. R. S. Ellis and M. A. Pinsky, The first and second fluid approximations to the linearized Boltzmann equation, J. Math. Pures et Appl. 54, 125–156 (1972).

    MathSciNet  Google Scholar 

  3. H. Grad, Asymptotic equivalence of the Navier-Stokes and nonlinear Boltzmann equations, Proc. Symp. Appl. Math. 17, R. Finn Ed., 154–183, AMS, Providence (1965).

    Google Scholar 

  4. T. Kato, Perturbation Theory of Linear Operators, Springer, New York (1966).

    Google Scholar 

  5. N. B. Maslova and A. N. Firsov, Solution of the Cauchy problem for the Boltzmann equation (in Russian), Vestnik Leningrad Univ. 19, 83–85 (1975).

    MATH  MathSciNet  Google Scholar 

  6. J. A. McLennan, Convergence of the Chapman-Enskog expansion for the linearized Boltzmann equation, Phys. Fluids 8, 1580–1584 (1965).

    Article  MathSciNet  Google Scholar 

  7. T. Nishida and K. Imai, Global solutions to the initial value problem for the non-linear Boltzmann equation, Publ. R.I.M.S. Kyoto Univ. 12, 229–239 (1976).

    MATH  MathSciNet  Google Scholar 

  8. E. C. Titchmarsh, Introduction to the Theory of Fourier Integral, Oxford University Press (1948).

    Google Scholar 

  9. S. Ukai, On the existence of global solutions of a mixed problem for the nonlinear Boltzmann equation, Proc. Japan Acad. 50, 179–184 (1974).

    Article  MATH  MathSciNet  Google Scholar 

  10. 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, 282A, 317–320 (1976).

    MathSciNet  Google Scholar 

  11. S. Ukai and Asano, On the Cauchy problem of the Boltzmann equation with a soft potential, Publ. R.I.M.S. Kyoto Univ. 18, 477–519 (1982).

    MATH  MathSciNet  Google Scholar 

  12. S. Ukai, Solutions of the Boltzmann equation in Patterns and Waves — Qualitative Analysis of Nonlinear Differential Equations, Studies in Mathematics and its Applications 18, 37–96 (1986).

    MATH  MathSciNet  Google Scholar 

Download references

Rights and permissions

Reprints and permissions

Copyright information

© 2006 Birkhäuser Verlag

About this chapter

Cite this chapter

(2006). Perturbations of Equilibria. In: Slow Rarefied Flows. Progress in Mathematical Physics, vol 41. Birkhäuser Basel. https://doi.org/10.1007/3-7643-7537-X_3

Download citation

Publish with us

Policies and ethics