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L p-Stability Theory of the Boltzmann Equation Near Vacuum

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Hyperbolic Problems: Theory, Numerics, Applications

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References

  1. Arkeryd, L.: Stability in L 1 for the spatially homogeneous Boltzmann equation. Arch. Rational Mech. Anal. 103, 151–168 (1988)

    Article  MATH  MathSciNet  Google Scholar 

  2. Arkeryd, L.: L ∞-estimates for the space homogeneous Boltzmann equation. J. Stat. Phys. 31, 347–361 (1982)

    Article  MathSciNet  Google Scholar 

  3. Bellomo, N., Toscani, G.: On the Cauchy problem for the nonlinear Boltzmann equation: global existence, uniqueness and asymptotic behavior. J. Math. Phys. 26, 334–338 (1985)

    Article  MATH  MathSciNet  Google Scholar 

  4. Chae, M., Ha, S.-Y.: Stability estimates of the Boltzmann equation with quantum effects. Contin. Mech. Thermodyn. 17, 511–524 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  5. Desvillettes, L., Mouhot, C.: About L p estimates for the spatially homogeneous Boltzmann equation. Ann. Inst. H. Poincare Anal. Non Lineaire 22, 127–142 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  6. Duan, R., Yang, T., Zhu, C.: L 1 and BV-type stability of the Boltzmann equation with external forces. J. Differential Equations 227, 1–28 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  7. Gustafsson, T.: L p-estimates for the nonlinear spatially homogeneous Boltzmann equation. Arch. Rational Mech. Anal. 92, 23–57 (1997)

    MathSciNet  Google Scholar 

  8. Gustafsson, T.: Global L p-properties for the spatially homogeneous Boltzmann equation. Arch. Rational. Mech. Anal. 103, 1–38 (1988)

    Article  MATH  MathSciNet  Google Scholar 

  9. Guo, Y.: The Boltzmann equation in the whole space. Indiana Univ. Math. J. 53, 1081–1094 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  10. Ha, S.-Y.: Nonlinear functionals of the Boltzmann equation and uniform stability estimates. J. Differential Equations 215, 178–205 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  11. Ha, S.-Y.: L 1 stability of the Boltzmann equation for the hard sphere model. Arch. Rational Mech. Anal. 173, 279–296 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  12. Ha, S.-Y., Yun, S.-B.: Uniform L 1-stability estimates of the Boltzmann equation near a local Maxwellian. Physica D 120, 79–97 (2006)

    Article  MathSciNet  Google Scholar 

  13. Ha, S.-Y., Yamazaki, M., Yun, S.-B.: Uniform L p-stability estimate for the spatially inhomogeneous Boltzmann equation near vacuum. Submitted.

    Google Scholar 

  14. Hamdache, K.: Existence in the large and asymptotic behavior for the Boltzmann equation. Japan. J. Appl. Math. 2, 1–15 (1984)

    Article  MathSciNet  Google Scholar 

  15. Illner, R., Shinbrot, M.: Global existence for a rare gas in an infinite vacuum. Commun. Math. Phys. 95, 217–226 (1984)

    Article  MATH  MathSciNet  Google Scholar 

  16. Kaniel, S., Shinbrot, M.: The Boltzmann equation 1: Uniqueness and local existence. Commun. Math. Phys. 58, 65–84 (1978)

    Article  MATH  MathSciNet  Google Scholar 

  17. Liu, T.-P., Yang, T., Yu, S.-H.: Energy method for Boltzmann equation. Physica D 188, 178–192 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  18. Lu, X.: Spatial decay solutions of the Boltzmann equation: converse properties of long time limiting behavior. SIAM J. Math. Anal. 30, 1151–1174 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  19. Mouhot, C., Villani, C.: Regularity theory for the spatially homogeneous Boltzmann equation with cut-off. Arch. Rational Mech. Anal. 173, 169–212 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  20. Polewczak, J.: Classical solution of the nonlinear Boltzmann equation in all R 3: asymptotic behavior of solutions. J. Stat. Phys. 50, 611–632 (1988)

    Article  MATH  MathSciNet  Google Scholar 

  21. Toscani, G.: Global solution of the initial value problem for the Boltzmann equation near a local Maxwellian. Arch. Rational Mech. Anal. 102, 231–241 (1988)

    Article  MATH  MathSciNet  Google Scholar 

  22. Toscani, G.: H-theorem and asymptotic trend of the solution for a rarefied gas in a vacuum. Arch. Rational Mech. Anal. 100, 1–12 (1987)

    Article  MathSciNet  Google Scholar 

  23. Toscani, G.: On the nonlinear Boltzmann equation in unbounded domains. Arch. Rational Mech. Anal. 95, 37–49 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  24. Ukai, S., Yang, T.: The Boltzmann equation in the space L 2 ∩ L β ∞: global and time-periodic solutions. Anal. Appl. (Singap.) 4(3), 263–310 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  25. Ukai, S., Yang, T.: Mathematical theory of Boltzmann equation. Lecture notes series-no. 8, Liu Bie Ju Center for Math. Sci. City University of Hong Kong, 2006

    Google Scholar 

  26. Wennberg, B.: Stability and exponential convergence for the Boltzmann equation. Arch. Rational Mech. Anal. 130, 103–144 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  27. Wennberg, B.: Stability and exponential convergence in L p for the spatially homogeneous Boltzmann equation. Nonlinear Anal. TMA, 20, 935–964 (1993)

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematical Sciences, Seoul National University, Seoul, 151-747, Republic of Korea

    S. -Y. Ha & S. -B. Yun

  2. Graduate School of Pure and Applied Sciences, University of Tsukuba, 305-8571, Ibaraki, Japan

    M. Yamazaki

Authors
  1. S. -Y. Ha
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  2. M. Yamazaki
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  3. S. -B. Yun
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Editor information

Editors and Affiliations

  1. Institut Camille Jordan UMR CNRS 5208, Université Claude Bernard Lyon 1, 43, Bd du, 69622, Villeurbanne cedex, France

    Sylvie Benzoni-Gavage

  2. UMPA, UMR CNRS 5669, Ecole Normale Supérieure de Lyon, 46, allée d'ltalie, 69364, Lyon cedex 07, France

    Denis Serre

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Ha, S.Y., Yamazaki, M., Yun, S.B. (2008). L p-Stability Theory of the Boltzmann Equation Near Vacuum. In: Benzoni-Gavage, S., Serre, D. (eds) Hyperbolic Problems: Theory, Numerics, Applications. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-75712-2_10

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