Quasineutral Limit of Euler-Poisson System with and without Viscosity

Communications in Partial Differential Equations

Volumn 29, Issue 3-4, 2005, Pages 419-456

  Wang, Shu ^a,b  

^a BEIJING UNIVERSITY OF TECHNOLOGY   (China)

^b UNIVERSITY OF VIENNA   (Austria)

Author keywords

Euler Poisson system; Incompressible Euler equations; Incompressible Navier Stokes equations; Quasineutral limit; Viscosity

Indexed keywords

EID: 1842733303     PISSN: 03605302     EISSN: None     Source Type: Journal    
DOI: 10.1081/pde-120030403     Document Type: Article

References (35)

1. Brenier, Y. (2000). Conference of the Vlasov-Poisson system to the incompressible Euler equations. Commun. Partial Diff. Eqs. 25:737-754.
2. Chen, G. Q., Glimm, J. (1996). Global solution to the compressible Euler equations with geometrical structure. Comm. Math. Phys. 180:153-193.
3. Chen, G. Q., Wang, D. (1996). Conference of shock capturing schemes for the compressible Euler-Poisson equation. Commun. Math. Phys. 179:333-364.
4. Cordier, S., Degond, P., Markowich, P., Schmeiser, C. (1995). A travelling wave analysis of a hydrodynamical model of quasineutral plasma. Asymptotic Anal. 11:209-224.
5. Cordier, S., Grenier, E. (1997). Quasineutral limit of two species Euler-Poisson systems. In: Proceedings of the Workshop "Recent Progress in the Mathematical Theory on Vlasov-Maxwell Equations". Paris, pp. 95-122.
6. Cordier, S., Grenier, E. (2000). Quasineutral limit of an Euler-Poisson system arising from plasma physics. Comm. PDE 23:1099-1113.
7. Degond, P. (2000). Mathematical modelling of microelectronics semiconductor devices. In: Some Current Topics on Nonlinear Conservation Laws, AMS/IP Stud. Adv. Math. 15, Providence, RI: Amer. Math. Soc., pp. 77-110.
8. Degond, P., Markowich, P. A. (1993). A steady-state potential flow model for semiconductors. Ann. Mat. Pura Appl. IV:87-98.
9. Gasser, I., Hsiao, L., Markowich, P., Wang, S. (2002). Quasineutral limit of a nonlinear drift-diffusion model for semiconductor models. J. Math. Anal. Appl. 268:184-199.
10. Gasser, I., Levermore, C. D., Markowich, P., Schmeiser, C. (2001). The initial time layer problem and the quasineutral limit in the semiconductor drift-diffusion model. Europ. J. Appl. Math. 12:497-512.
11. 3+1. Comm. Math. Phys. 195:249-265.
12. Grenier, E. (1995). Defect measures of the Vlasov-Poisson system. Commun. Partial Diff. Eqs. 20:1189-1215.
13. Grenier, E. (1996). Oscillations in quasineutral plasmas. Commun. Partial Diff. Eqs. 21:363-394.
14. Grenier, E. (1997a). Pseudodifferential estimates of singular perturbations. Commun. Pure Appl. Math. 50:821-865.
15. Grenier, E. (1997b). Oscillartory perturbations of the Navier-Stokes equations. Journal de Maths Pures et appl. (9) 76:477-498.
16. Jüngel, A., Peng, Y.-J. (2001). A hierarchy of hydrodynamic models for plasmas: Quasi-neutral limits in the drift-diffusion equations. Asympt. Anal. 28:49-73.
17. Hsiao, L., Markowich, P. A., Wang, S. (2003). The asymptotic behavior of globally smooth solutions of the multidimensional isentropic hydrodynamic model for semiconductors. J. Diff. Eqns. 192:111-133.
18. 3. J. Funct. Anal. 9:296-305.
19. Kato, T. (1975). The Cauchy problem for quasilinear symmetric systems. Arch. Rational Mech. Anal. 58:181-205.
20. Klainerman, S., Majda, A. (1981). Singular limits of quasilinear hyperbolic systems with large parameters and the incompressible limit of compressible fluids. Comm. Pure and Appl. Math. XXXIV:481-524.
21. Klainerman, S., Majda, A. (1982). Compressible and incompressible fluids. Comm. Pure and Appl. Math. XXXV:629-651.
22. Majda, A. (1984). Compressible Fluid Flow and Systems of Conservation Laws in Several Space Variables. Berlin: Springer-Verlag.
23. Makino, T., Ukai, S. (1987). Sur l'existence des solutions locales de l'équation d'Euler-Poisson pour l'évolution d'étoiles gazeuses. J. Math. Kyoto Univ. 27:387-399.
24. Makino, T., Mizohata, K., Ukai, S. (1992). The global weak solutions of compressible Euler equations with spherical symmetry. Japan J. Industrial Appl. Math. 9:431-449.
25. Marcati, P. A., Natalini, R. (1995). Weak solutions to hydrodynamic model for semiconductors and relaxation to the drift-diffusion equation. Arch. Rational Mech. Anal. 129:129-145.
26. Markowich, P. A., Ringhofer, C., Schmeiser, C. (1990). Semiconductors Equations. Vienna, New York: Springer-Verlag.
27. Masmoudi, N. (2000). Ekman layers of rotating fluids, the case of general initial data. Commun. Pure and Appl. Math. LIII:432-483.
28. Masmoudi, N. (2001). From Vlasov-Poisson system to the incompressible Euler system. Comm. Partial Differential Equations 26:1913-1928.
29. McGrath, F. J. (1968). Nonstationary plane flow of viscous and ideal fluds. Arch. Rational Mech. Anal. 27:229-348.
30. Poupaud, F., Rascle, M., Vila, J. P. (1995). Global solutions to the isothermal Euler-Poisson system with arbitrary large data. J. Diff. Eqns. 129:93-121.
31. Schochet, S. (1994). Fast singular limits of hyperbolic PDEs. J. Diff. Eqns. 114:476-512.
32. Sideris, T. (1991). The lifespan of smooth solutions to the three-dimensional compressible Euler equations and the incompressible limit. Indiana Univ. Math. J. 40:536-550.
33. 3. Trans. of Amer. Math. Soc. 157:373-397.
34. Ukai, S. (1986). The incompressible limit and the initial layer of the compressible Euler equation. J. Math. Kyoto Univ. 26:323-331.
35. Zhang, B. (1993). Convergence of the Godunov scheme for a simplified one-dimensional hydrodynamic model for semiconductor devices. Comm. Math. Phys. 157:1-22.