Advanced Search
Article Contents
Article Contents

Transport coefficients in the $2$-dimensional Boltzmann equation

Abstract Related Papers Cited by
  • We show that a rarefied system of hard disks in a plane, described in the Boltzmann-Grad limit by the $2$-dimensional Boltzmann equation, has bounded transport coefficients. This is proved by showing opportune compactness properties of the gain part of the linearized Boltzmann operator.
    Mathematics Subject Classification: 76P05, 82C40, 76A20.


    \begin{equation} \\ \end{equation}
  • [1]

    G. Basile, C. Bernardin and S. Olla, Thermal conductivity for a momentum conserving model, Commun. in Mathematical Physics, 287 (2009), 67-98.doi: 10.1007/s00220-008-0662-7.


    C. Cercignani, R. Illner and M. Pulvirenti, The Mathematical Theory of Dilute Gases, Applied Mathematical Sciences, 106. Springer-Verlag, New York, 1994.


    R. Esposito and M. Pulvirenti, Rigorous validity of the Boltzmann equation for a thin layer of a rarefied gas, Kinetic and Related Models, 3 (2010), 281-297.doi: 10.3934/krm.2010.3.281.


    D.T. Morelli, J. Heremans, M. Sakamoto and C. Uher, Anisotropic heat conduction in diacetylenes, Phys. Rev. Lett., 57 (1986), 869-872.doi: 10.1103/PhysRevLett.57.869.


    O. E. Lanford III, The evolution of Large Classical systems, in Dynamical Systems, Theory and Applications, J. Moser ed., Lecture Notes in Physics, Springer Berlin, 38 (1975), 1-111.


    J. C. Maxwell, On the dynamical theory of gases, Phil. Trans. Royal Soc. London, 157 (1867), 49-88.


    A. Smontara, J. C. Lasjaunas and R. Maynard, Phonon poiseuille flow in quasi-one-dimensional single crystals, Phys. Rev. Lett., 77 (1996), 5397-5400.doi: 10.1103/PhysRevLett.77.5397.


    A. V. Sologubenko, K. Giann H. R. Ott, A. Vietkine and A. Revcolevschi, Heat transport by lattice and spin excitations in the spin-chain compounds $SrCuO_2$ and $Sr_2CuO_3$, Phys. Rev. B, 64 (2001), 054412.


    S.Ukai, On the spectrum of the space-independent Boltzmann operator, J. Nuclear Energy, Parts A/B, 19 (1965), 833-848.


    S.Ukai, On the existence of global solution of mixed problem for non-linear Boltzmann equation, Proc. Japan. Acad., 50 (1974), 179-184.doi: 10.3792/pja/1195519027.


    V. S. Vladimirov, Equations of Mathematical Physics, Translated from the Russian by Audrey Littlewood. Edited by Alan Jeffrey. Pure and Applied Mathematics, 3 Marcel Dekker, Inc., New York 1971.

  • 加载中

Article Metrics

HTML views() PDF downloads(68) Cited by(0)

Access History

Other Articles By Authors



    DownLoad:  Full-Size Img  PowerPoint