On the spatially homogeneous Boltzmann equation
Mischler, Stéphane ; Wennberg, Bernst
Annales de l'I.H.P. Analyse non linéaire, Tome 16 (1999), p. 467-501 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU) 
@article{AIHPC_1999__16_4_467_0,
     author = {Mischler, St\'ephane and Wennberg, Bernst},
     title = {On the spatially homogeneous Boltzmann equation},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     volume = {16},
     year = {1999},
     pages = {467-501},
     mrnumber = {1697562},
     zbl = {0946.35075},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPC_1999__16_4_467_0}
}

Mischler, Stéphane; Wennberg, Bernst. On the spatially homogeneous Boltzmann equation. Annales de l'I.H.P. Analyse non linéaire, Tome 16 (1999) pp. 467-501. http://gdmltest.u-ga.fr/item/AIHPC_1999__16_4_467_0/

[1] L. Arkeryd, On the Boltzmann equation, Arch. Rational Mech. Anal., Vol. 34, 1972, pp. 1-34. | MR 339665 | Zbl 0245.76059

[2] T. Carleman, Problèmes mathématiques dans la théorie cinétique des gaz, Almqvist and Wiksell, Uppsala, 1957. | MR 98477 | Zbl 0077.23401

[3] C. Cercignani, The theory and application of the Boltzmann equation, Springer, New York, 1988.

[4] C. Cercignani, R. Illner and M. Pulvirenti, The Mathematical Theory of Dilute Gases, Springer, New York, 1994. | MR 1307620 | Zbl 0813.76001

[5] L. Desvillettes, Some applications of the method of moments for the homogeneous Boltzmann and Kac equation, Arch. Rational Mech. Anal., Vol. 123, n° 4, 1993, pp. 387-395. | MR 1233644 | Zbl 0784.76081

[6] G. Diblasio, Differentiability of spatially homogeneous solutions of the Boltzmann equation Commun. Math. Phys., Vol. 38, 1974, pp. 331-340. | MR 356798 | Zbl 0298.35050

[7] T. Elmroth, Global boundedness of moments of solutions of the Boltzmann equation for forces of infinite range, Arch. Rational Mech. Anal., Vol. 82, 1983, pp. 1-12. | MR 684411 | Zbl 0503.76091

[8] E. Gabetta, L. Pareschi and G. Toscani, Relaxation schemes for nonlinear kinetic equations, SIAM J. Num. Anal., Vol. 34, 1997, pp. 2168-2194. | MR 1480374 | Zbl 0897.76071

[9] T. Gustafsson, Global Lp-properties for the spatially homogeneous Boltzmann equation, Arch. Rational Mech. Anal., Vol. 103, 1988, pp. 1-38. | MR 946968 | Zbl 0656.76067

[10] P.-L. Lions, Compactness in Boltzmann's equation via Fourier integral operators and applications I-III, J. Math. Kyoto Univ., Vol. 34, n°. 2, pp. 391-427, pp. 429-461, and n° 3, 1994, pp. 539-584. | Zbl 0831.35139

[11] A.J. Povzner, About the Boltzmann equation in kinetic gas theory, Mat. Sborn, Vol. 58, 1962, pp. 65-86. | MR 142362 | Zbl 0188.21204

[12] E. Ringeisen, Contributions à l'étude Mathématique des Equations Cinétiques, Ph. D-thesis, Université Paris 7, Paris, 1991.

[13] B. Wennberg, On moments and uniqueness for solutions to the space homogeneous Boltzmann equation, Transport Theory Stat. Phys., Vol. 24 (4), 1994, pp. 533-539. | MR 1264851 | Zbl 0812.76080

[14] B. Wennberg, Entropy dissipation and moment production for the Boltzmann equation, to appear in J. Statist. Phys. | MR 1450762 | Zbl 0935.82035

[15] B. Wennberg, The Povzner inequality and moments in the Boltzmann equation, Rendiconti del Circolo Matematico di Palermo, Ser II, suppl. 45, 1996, pp. 673-681. | MR 1461113 | Zbl 0909.76089