Oscillations in quasineutral plasmas

Communications in Partial Differential Equations

Volumn 21, Issue 3-4, 1996, Pages 363-394

  Grenier, Emmanuel ^a  

^a ECOLE NORMALE SUPÉRIEURE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0005604229     PISSN: 03605302     EISSN: None     Source Type: Journal    
DOI: 10.1080/03605309608821189     Document Type: Article

References (20)

1. S. Alinhac : Approximation et temps de vie des solutions des équations d'Euler isentropiques en dimension 2 d'espace, Séminaire sur les équations aux dérivées partielles, École Polytechnique, Palaiseau (France) 90-91, exposé no7.
2. S. Alinhac : Temps de vie des solutions régulières des équations d'Euler compressibles axisymétriques en dimension deux. Invent. math. no111 (1993), p627-670.
3. C. Bardos, P. Degond : Global existence for the Vlasov-Poisson equation in 3 space variables with small initial data. Ann. Inst. Henri. Poincaré, Anal. non linéaire 2 (1985) p101-118.
4. S. Benachour : Analycité des solutions des équations de Vlasov-Poisson Ann. Scuola. Norm. Sup. Pisa Cl.Sci (4) 16 (1989) no1 p83-104.
5. H. L. Berk, C. E. Nielsen, K. V. Roberts : phase space hydrodynamics of equivalent nonlinear systems : experimental and computational Observations Phys. of Fluids 13(4) (1967) p980-995.
6. A. Bensoussan, J.-L. Lions, G. Papanicolaou : Asymptotic Analysis for periodic structures, Studies in Math. and its applications, 5, North Holland, 1978.
7. Y. Brenier : A Vlasov-Poisson type formulation of the Euler equations, rapport INRIA 1070 (1989).
8. Y. Brenier : The Least Action Principle and the related concept of generalized flows for incompressible fluids, J. Amer. Math. Soc. 2 (1990) p225-255.
9. Y. Brenier, E. Grenier : Limite singulière du système de Vlasov-Poisson dans le régime de quasi neutralité : le cas indépendant du temps, C. R. Acad. Sci. Paris Sér. I Math, t.318 (1994), p.121-124.
10. G. Browning, H.-O. Kreiss : Problems with different time scales for nonlinear partial differential equations, Siam J. Appl. Math. 42 (1982) p704-718.
11. R. Caflisch : A simplified version of the abstract Cauchy-Kovalevski Theorem with weak singularities, Bull. Amer. Math. Soc. 23 (2) (1990) p495-500.
12. D.G. Ebin : Motion of slightly compressible fluids in a bounded domain I, Comm. Pure Appl. Math. 35 (1982) p451-485.
13. E. Grenier : Defect measures of the Vlasov-Poisson system in the quasineutral regime, to appear in Comm. Partial Differential Equations.
14. S. Klainerman, A. Majda : Compressible and Incompressible fluids, Comm. Pure Appl. Math. 35 (1982) p629-651.
15. J.-L. Lions : Perturbations singulières, Lectures Notes in Mathematics, 323, Springer-Verlag, 1973.
16. P.-L. Lions : Limites incompressible et acoustique pour des fluides visqueux, compressibles et isentropiques, C. R. Acad. Sci. Paris Sér. I Math. t317 (1993) p1197-1202.
17. K. Pfaffelmoser : Global classical solutions of the Vlasov-Poisson system in 3D for general initial data, J. Differential Equations 95 (1992) p281-303.
18. T. Sideris : The lifespan of smooth solutions to the 3D compressible Euler equations and the incompressible limit, Indiana Univ. Math. J. Vol 40 (1991) p535-550.
19. S. Ukai and T. Okabe : On classical solution in the large in time of two-dimensional Vlasov's equation, Osaka J. Math. 15 (1978) no2 p245-261.
20. S. Ukai : The incompressible limit and the initial layer of the compressible Euler equation, J. Math. Kyoto Univ , 26 (1986) p497-506.