The Vlasov-Maxwell-Boltzmann system near Maxwellians

Inventiones Mathematicae

Volumn 153, Issue 3, 2003, Pages 593-630

  Guo, Yan ^a  

^a BROWN UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0041413233     PISSN: 00209910     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00222-003-0301-z     Document Type: Article

References (15)

1. [C] Cercignani, C.: The Boltzmann Equation and Its Application. Springer-Verlag 1988
2. [CIP] Cercignani, C., Illner, R., Pulvirenti, M.: The Mathematical Theory of Dilute Gases. Springer-Verlag 1994
3. [Ch] Chapman, S., Cowling, T.G.: The Mathematical Theory of Non-uniform Gases. Cambridge 1952
4. [DD] Desvilletes, L., Dolbeault, J.: On long time asymptotics of the Vlasov-Poisson-Boltzmann equation. Commun. Partial Differ. Equations 16, 451-489 (1991)
5. [DL1] Diperna, R., Lions, P.-L.: On the Cauchy problem for the Boltzmann equation: global existence and weak stability. Ann. Math. (2) 130, 321-366 (1989)
6. [DL2] Diperna, R., Lions, P.-L.: Ordinary differential equations, transport theory and Sobolev spaces. Invent. Math. 98, 511-547 (1989)
7. [L] Lions, P.-L.: Global solutions of kinetic models and related equations. Nonequilib- rium problems in many-particle systems. (Montecatini, 1992), 58-86. Lect. Notes Math. 1551. Berlin: Springer 1993
8. [G1] Quo, Y.: The Vlasov-Poisson-Boltzmann system near Maxwellians. Commun. Pure Appl. Math., Vol. LV, 1104-1135 (2002)
9. [G2] Guo, Y.: The Landau equation in aperiodic box. Commun. Math. Phys. 231, 391-434 (2002)
10. [G3] Guo, Y.: Classical solutions to the Boltzmann equation for molecules with an angular cutoff. Arch. Rational Mech. Anal, in press (2003)
11. [GL] Glassey, R.: The Cauchy Problems in Kinetic Theory. SIAM 1996
12. [GS1] Glassey, R., Strauss, W.: Decay of the linearized Boltzmann-Vlasov system. Trans. theory Stat. Phys. 28, 135-156 (1999)
13. [GS2] Glassey, R., Strauss, W.: Perturbation of essential spectra of evolution operators and the Vlasov-Poisson-Boltzmann system. Discrete Contin. Dyn. Syst. 5, 457-472 (1999)
14. [M] Mischler, S.: On the initial boundary value problem for the Vlasov-Poisson-Boltzmann system. Commun. Math. Phys. 210, 447-466 (2000)
15. [U] Ukai, S.: On the existence of global solutions of a mixed problem for the nonlinear Boltzmann equation. Proc. Japan Acad., Ser. A 53, 179-184 (1974)