Skip to main content
SpringerLink
Log in

Steady solutions of the Boltzmann equation for a gas flow past an obstacle, I. Existence

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

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

References

  1. Asano, K.; On the initial boundary value problem of the nonlinear Boltzmann equation in an exterior domain, (to appear).

  2. Bergh, J., & J. Löfström; “Interpolation Spaces, An Introduction”, Springer-Verlag, Berlin, Heidelberg, New York 1976.

    Google Scholar 

  3. Brezis, H., & G. Stampacchia; The hodograph method in fluid dynamics in the light of variational inequalities, Arch. Rational Mech. Anal., 61, 1–18 (1976).

    Google Scholar 

  4. Carleman, T.; “Problèmes Mathématiques dans la Théorie Cinétique des Gaz”, Almquist & Wiksell, Uppsala, 1957.

    Google Scholar 

  5. Ellis, R. S., & M. A. Pinsky; The first and second fluid approximations to the linearized Boltzmann equation, J. Math. Pures et Appl., 54, 125–156 (1975).

    Google Scholar 

  6. Giraud, J. P.; An H theorem for a gas of rigid spheres, Théories Cinétiques Classiques et Relativistes, C. N. R. S. Paris (1975).

    Google Scholar 

  7. Grad, H.; Asymptotic theory of the Boltzmann equation, Rarefied Gas Dynamics, I (J. A. Laurman, ed.), Academic Press, New York, 1963.

    Google Scholar 

  8. Grad, H.; Asymptotic equivalence of the Navier-Stokes and nonlinear Boltzmann equations, Proc. Symp. Appl. Math., 17 (R. Finn, ed.), 154–183, Amer. Math. Soc., Providence, 1965.

  9. Kaniel, S., & M. Shinbrot; The Boltzmann equation I, Comm. Math. Phys., 57, 1–20 (1978).

    Google Scholar 

  10. Kato, T.; “Perturbation Theory of Linear Operators”, 1st Ed., Springer-Verlag, Berlin, Heidelberg, New York, 1966.

    Google Scholar 

  11. Matsumura, A., & T. Nishida; Global solutions to the initial boundary value problem for the equation of compressible, viscous and heat conductive fluids, to appear.

  12. Morawetz, C.; Mixed equations and transonic flows, Rend. Math., 25, 482–509 (1966).

    Google Scholar 

  13. Shizuta, Y. (private communication).

  14. Ukai, S., & K. Asano; On the initial boundary value problem of the linearized Boltzmann equation in an exterior domain, Proc. Japan Acad., 56, 12–17 (1980).

    Google Scholar 

  15. Ukai, S., & K. Asano; On the existence and stability of stationary solutions of the Boltzmann equation for a gas flow past an obstacle, Research Notes in Mathematics, Pitman, 60, 350–364 (1982).

    Google Scholar 

  16. Ukai, S., & K. Asano; Stationary solutions of the Boltzmann equation for a gas flow past an obstacle, II. Stability, preprint.

Download references

Author information

Authors and Affiliations

  1. Department of Applied Physics, Osaka City University, USA

    Seiji Ukai & Kiyoshi Asano

  2. Institute of Mathematics Yoshida College Kyoto University, USA

    Seiji Ukai & Kiyoshi Asano

Authors
  1. Seiji Ukai
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Kiyoshi Asano
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Communicated by J. L. Lions

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ukai, S., Asano, K. Steady solutions of the Boltzmann equation for a gas flow past an obstacle, I. Existence. Arch. Rational Mech. Anal. 84, 249–291 (1983). https://doi.org/10.1007/BF00281521

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00281521

Keywords

Search

Navigation