C0 Approximation on the Spatially Homogeneous Boltzmann Equation for Maxwellian Molecules

Minling Zheng^{*}

References

[1] H. L. Li and A. Matsumura, “Behaviour of the Fokker- Planck-Boltzmann Equation near a Maxwellian,” Archive for Rational Mechanics and Analysis, Vol. 189, No. 1, 2008, pp. 1-44.

[2]
M. Zheng and X. P. Yang, “Viscosity Analysis on the Spatially Homogeneous Botzmann Equation,” Asymptotic Analysis, Vol. 53, 2007, pp. 13-28.

[3]
L. Arkeryd, “On the Boltzmann Equation,” Archive for Rational Mechanics and Analysis, Vol. 45, 1972, pp. 1-34.

[4] L. Arkeryd, “Stability in L1 for the Spatially Homogeneous Boltzmann Equation,” Archive for Rational Mechanics and Analysis, Vol. 103, 1988, pp. 151-167.

[5] T. Elmroth, “Global Boundedness of Moments of Solution of the Boltzmann Equation for Forces of Infinite Range,” Archive for Rational Mechanics and Analysis, Vol. 82, 1983, pp. 1-12.

[6] L. Desvillettes, “Some Applications of the Method of Moments for the Homogeneous Boltzmann Equation and Kac Equation,” Archive for Rational Mechanics and Analysis, Vol. 123, 1993, pp. 387-395.

[7] S. Mischler and B. Wennberg, “On the Spatially Homogeneous Boltzmann Equaion,” Annales de l’Institut Henri Poincar′e - Analyse non lin′eaire, Vol. 16, No. 4, 1999, pp. 467-501.

[8]
B. Wennberg, “Entropy Dissipation and Moment Production for the Boltzmann Equation,” Journal of Statistical Physics, Vol. 86, 1997, pp. 1053-1066.

[9]
B. Wennberg, “Stability and Exponential Convergence in Lp for the Spatially Homogeneous Boltzmann Equation,” Nonlinear Analysis, Theory, Methods & Applications, Vol. 20, 1993, pp. 935-964.

[10]
C. Mouhot and C. Villani, “Regularity Theory for the Spatially Homogeneous Boltzmann Equation with Cut- off,” Archive for Rational Mechanics and Analysis, Vol. 173, No. 2, 2004, pp. 169-212.

[11]
C. Mouhot, “Rate of Convergence to Equalibrium for the Spatially Homogeneous Boltzmann Equation with Hard Potentials,” Communications in Mathematical Physics, Vol. 261, 2006, pp. 629-672.

[12] D. Morgenstern, “General Existence and Uniqueness Proof for Spatial Homogeneous Solution of the Maxwell-Boltzm-ann Equation in the Case of Maxwellian Molecules,” Proceedings of the National Academy of Sciences, Vol. 40, 1954, pp. 719-721.

[13]
R. J. DiPerna and P. L. Lions, “On the Fokker-Planck- Boltzmann Equation,” Communications in Mathematical Physics, Vol. 120, No. 1, 1988, pp. 1-23.

[14]
I. M. Gamba, V. Panferno and C. Villani, “On the Boltzmann Equation for Diffusively Excited Granular Media,” Communications in Mathematical Physics, Vol. 246, No. 3, 2004, pp. 503-541