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

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References

  1. 1.

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

  2. 2.

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

  3. 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).

  4. 4.

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

  5. 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).

  6. 6.

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

  7. 7.

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

  8. 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. 9.

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

  10. 10.

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

  11. 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. 12.

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

  13. 13.

    Shizuta, Y. (private communication).

  14. 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).

  15. 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).

  16. 16.

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

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Communicated by J. L. Lions

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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

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Keywords

  • Neural Network
  • Complex System
  • Nonlinear Dynamics
  • Boltzmann Equation
  • Electromagnetism