On the stationary Boltzmann equation
Arkeryd, Leif1
1 Department of Mathematics, Chalmers Institute of Technology, S-41296 Gothenburg, Sweden
Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" (2001-2002), Exposé no. 1, 11 p.

For stationary kinetic equations, entropy dissipation can sometimes be used in existence proofs similarly to entropy in the time dependent situation. Recent results in this spirit obtained in collaboration with A. Nouri, are here presented for the nonlinear stationary Boltzmann equation in bounded domains of IR n with given indata and diffuse reflection on the boundary.

Arkeryd, Leif 1

1 Department of Mathematics, Chalmers Institute of Technology, S-41296 Gothenburg, Sweden 
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Arkeryd, Leif. On the stationary Boltzmann equation. Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" (2001-2002), Exposé no. 1, 11 p. http://www.numdam.org/item/SEDP_2001-2002____A1_0/

[1] Arkeryd, L., Cercignani, C., ’On the convergence of solutions of the Enskog equation to solutions of the Boltzmann equation’, Comm. Part. Diff. Eqns. 14, 1989, 1071-1089. | Zbl

[2] A rkeryd, L., Nouri, A., ’The stationary Boltzmann equation in the slab with given weighted mass for hard and soft forces’, Ann. Scuola Norm. Sup. Pisa Cl. Sci. 27, 1998, 533-556. | Numdam | Zbl

[3] Arkeryd, L., Nouri, A., ’On the stationary Povzner equation in three space variables’, J. Math. Kyoto Univ. 39, 1999, 115-153. | Zbl

[4] Arkeryd, L., Nouri, A., ’L 1 solutions to the stationary Boltzmann equation in a slab’, Ann. Fac. Sci. Toulouse Math. 9, 2000, 375-413. | Numdam | Zbl

[5] Arkeryd, L., Nouri, A., ’The stationary Boltzmann equation in IR n with given indata’, to appear in Ann. Scuola Norm. Sup. di Pisa. | Zbl

[6] Cercignani, C., Illner, R., Pulvirenti, M., ’The mathematical theory of dilute gases’, Springer -Verlag, Berlin, 1994. | Zbl

[7] DiPerna, R. J., Lions, P. L., ’On the Cauchy problem for Boltzmann equations: Global existence and weak stability’, Ann. Math. 130, 1989, 321-366. | Zbl

[8] DiPerna, R. J., Lions, P. L., Meyer, Y., ’L p regularity of velocity averages’, Anal. Non Lin. 8, 1991, 271-287. | Numdam | Zbl

[9] Grad, H., ’High frequency sound recording according to Boltzmann equation’, SIAM J. Appl. Math. 14, 1966, 935-955. | Zbl

[10] Guiraud, J. P., ’Problème aux limites intérieur pour l’équation de Boltzmann en régime stationaire, faiblement non linéaire’, J. Méc. Théor. Appl. 11, 1972, 183-231. | Zbl

[11] Heintz, A., in preparation.

[12] Maslova, N., ’Non linear evolution equations, Kinetic approach’, Series on Advances in Mathematics for Applied Sciences, Vol 10, World Scientific, 1993. | Zbl

[13] Panferov, V., ’On the existence of stationary solutions to the Povzner equation in a bounded domain’, 2000, submitted.

[14] Ukai, S., Asano, K., ’Steady solutions of the Boltzmann equation for a gas flow past an obstacle; I existence’, Arch. Rat. Mech. Anal. 84, 1983, 249-291. | Zbl