Macroscopic limit of Vlasov type equations with friction

Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire

Volumn 17, Issue 5, 2000, Pages 651-672

  Jabin, Pierre Emmanuel ^a  

^a ECOLE NORMALE SUPÉRIEURE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0005525756     PISSN: 02941449     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0294-1449(00)00118-9     Document Type: Article

References (18)

1. Allaire G., Homogenization and two-scale convergence, SIAM J. Math. Anal. XXIII (12) (1992) 1482-1518.
2. Arsenev A.A., Global existence of a weak solution of Vlasov's system of equations, USSR Comp. Math. and Math. Phys. 15 (1975) 131-141.
3. Brenier Y., Convergence of the Vlasov-Poisson system to the incompressible Euler equations, Comm. PDE, to appear.
4. DiPerna R.J., Lions P.L., Solutions globales d'équations du type Vlasov-Poisson, C.R. Acad. Sci. Paris Sér. I 307 (1988) 655-658.
5. Frénod E., Sonnendrücker E., Long time behaviour of the two-dimensional Vlasov equation with a strong external magnetic field, INRIA Report, 3428, 1998.
6. Gasser I., Jabin P.-E., Perthame B., Regularity and propagation of moments in some nonlinear Vlasov systems, Work in preparation.
7. Glassey R.T., The Cauchy Problem in Kinetic Theory, SIAM, Philadelphia, 1996.
8. Golse F., Saint-Raymond L., The Vlasov-Poisson system with strong magnetic field, LMENS 99 (2) (1999).
9. Grenier E., Defect measures of the Vlasov-Poisson system, Comm. PDE 21 (1996) 363-394.
10. N'Guetseng G., A general convergence result for a functional related to the theory of homogeneization, SIAM J. Math. Anal. 20 (1989) 608-623.
11. Hamdache K., Global existence and large time behaviour of solutions for the Vlasov-Stokes equations, Japan J. Indust. Appl. Math. 15 (1998) 51-74.
12. Herrero H., Lucquin-Desreux B., Perthame B., On the motion of dispersed bubbles in a potential flow, Siam J. Appl. Math, to appear.
13. Horst E., On the classical solutions of the initial value problem for the unmodified non-linear Vlasov equation, Math. Meth. in the Appl. Sci. 3 (1981) 229-248.
14. Jabin P.-E., Large time concentrations for solutions to kinetic equations with energy dissipation, Comm. PDE, to appear.
15. Jabin P.-E., Perthame B., Notes on mathematical problems on the dynamics of dispersed particles interacting through a fluid, in: Bellomo N., Pulvirenti M. (Eds.), Modelling in Applied Sciences, a Kinetic Theory Approach, to appear.
16. Rubinstein J., Keller J.B., Particle distribution functions in suspensions, Phys. Fluids A 1 (1989) 1632-1641.
17. Russo G., Smereka P., Kinetic theory for bubbly flow I and II, SIAM J. Appl. Math. 56 (1996) 327-371.
18. Sandor V., The Euler-Poisson system with pressure zero as singular limit of the Vlasov-Poisson system, the spherically symmetric case, Preprint.