On the spatially homogeneous Boltzmann equation

 Access to full text

 Full (PDF)

1. [1] L. Arkeryd, On the Boltzmann equation, Arch. Rational Mech. Anal., Vol. 34, 1972, pp. 1-34. Zbl0245.76059MR339665
2. [2] T. Carleman, Problèmes mathématiques dans la théorie cinétique des gaz, Almqvist and Wiksell, Uppsala, 1957. Zbl0077.23401MR98477
3. [3] C. Cercignani, The theory and application of the Boltzmann equation, Springer, New York, 1988. Zbl0646.76001
4. [4] C. Cercignani, R. Illner and M. Pulvirenti, The Mathematical Theory of Dilute Gases, Springer, New York, 1994. Zbl0813.76001MR1307620
5. [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. Zbl0784.76081MR1233644
6. [6] G. Diblasio, Differentiability of spatially homogeneous solutions of the Boltzmann equationCommun. Math. Phys., Vol. 38, 1974, pp. 331-340. Zbl0298.35050MR356798
7. [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. Zbl0503.76091MR684411
8. [8] E. Gabetta, L. Pareschi and G. Toscani, Relaxation schemes for nonlinear kinetic equations, SIAM J. Num. Anal., Vol. 34, 1997, pp. 2168-2194. Zbl0897.76071MR1480374
9. [9] T. Gustafsson, Global Lp-properties for the spatially homogeneous Boltzmann equation, Arch. Rational Mech. Anal., Vol. 103, 1988, pp. 1-38. Zbl0656.76067MR946968
10. [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. Zbl0831.35139
11. [11] A.J. Povzner, About the Boltzmann equation in kinetic gas theory, Mat. Sborn, Vol. 58, 1962, pp. 65-86. Zbl0188.21204MR142362
12. [12] E. Ringeisen, Contributions à l'étude Mathématique des Equations Cinétiques, Ph. D-thesis, Université Paris 7, Paris, 1991. 
13. [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. Zbl0812.76080MR1264851
14. [14] B. Wennberg, Entropy dissipation and moment production for the Boltzmann equation, to appear in J. Statist. Phys. Zbl0935.82035MR1450762
15. [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. Zbl0909.76089MR1461113

1. Laurent Desvillettes, Clément Mouhot, About $L^p$ estimates for the spatially homogeneous Boltzmann equation
2. M. Escobedo, S. Mischler, Dust and self-similarity for the Smoluchowski coagulation equation
3. T. Horsin, S. Mischler, A. Vasseur, On the convergence of numerical schemes for the Boltzmann equation
4. M. Escobedo, S. Mischler, M. Rodriguez Ricard, On self-similarity and stationary problem for fragmentation and coagulation models