A large data existence result for the stationary Boltzmann equation in a cylindrical geometry

Arkiv for Matematik

Volumn 43, Issue 1, 2005, Pages 29-50

  Arkeryd, Leif ^a   Nouri, Anne ^b  

^a UNIVERSITY OF GOTHENBURG   (Sweden)

^b AIX MARSEILLE UNIVERSITY   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 17444390955     PISSN: 00042080     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02383609     Document Type: Article

References (17)

1. ARKERYD, L. and CERCIGNANI, C., On the convergence of solutions of the Enskog equation to solutions of the Boltzmann equation, Comm. Partial Differential Equations 14 (1989), 1071-1089.
2. ARKERYD, L. and 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.
3. n, J. Math. Kyoto Univ. 39 (1999), 115-153.
4. 1 solutions to the stationary Boltzmann equation in a slab, Ann. Fac. Sci. Toulouse Math. 9 (2000), 375-413.
5. ARKERYD, L. and NOURI, A., On the Milne problem and the hydrodynamic limit for a steady Boltzmann equation model, J. Statist. Phys. 99 (2000), 993-1019.
6. n with given indata, Ann. Scuola Norm. Sup. Pisa Cl. Sci. 1 (2002), 359-385.
7. q-solutions and hydrodynamic limits, to appear in J. Statist. Phys.
8. CERCIGNANI, C., ILLNER, R. and PULVIRENTI, M., The Mathematical Theory of Dilute Gases, Applied Math. Sci., 106, Springer-Verlag, New York, 1994.
9. DIPERNA, R. J. and LIONS, P. -L., On the Cauchy problem for Boltzmann equations: global existence and weak stability, Ann. of Math. 130 (1989), 321-366.
10. GOLSE, F., LIONS, P. -L., PERTHAME, B. and SENTIS, R., Regularity of the moments of the solution of a transport equation, J. Funct. Anal. 76 (1988), 110-125.
11. GRAD, H., High frequency sound recording according to Boltzmann equation, SIAM J. Appl. Math. 14 (1966), 935-955.
12. GUIRAUD, J. -P., Problème aux limites intérieur pour l'équation de Boltzmann en régime stationaire, faiblement non linéaire, J. Mécanique 11 (1972), 183-231.
13. HEINTZ, A., Solvability of a boundary problem for the non linear Boltzmann equation in a bounded domain, in Molecular Gas Dynamics, Aerodynamics of Rarefied Gases 10, pp. 16-24, Leningrad, 1980 (Russian).
14. MASLOVA, N., Non Linear Evolution Equations, Kinetic Approach, Series on Advances in Mathematics for Applied Sciences 10, World Scientific, 1993.
15. PANFEROV, V., On the existence of stationary solutions to the Povzner equation in a bounded domain, to appear in Ann. Scuola Norm. Sup. Pisa Cl. Sci.
16. SONE, Y., Kinetic Theory and Fluid Dynamics, Birkhäuser, Boston, 2002.
17. UKAI, S. and ASANO, K., Steady solutions of the Boltzmann equation for a gas flow past an obstacle. I. Existence, Arch. Rational Mech. Anal. 84 (1983), 249-291.