Table of Contents
ISRN Applied Mathematics
Volume 2012 (2012), Article ID 581710, 7 pages
http://dx.doi.org/10.5402/2012/581710
Research Article

On a Quasi-Neutral Approximation of the Incompressible Navier-Stokes Equations

College of Mathematics and Information Science, North China University of Water Resources and Electric Power, Zhengzhou 450011, China

Received 21 June 2012; Accepted 10 October 2012

Academic Editors: R. Cardoso and X.-S. Yang

Copyright © 2012 Zhiqiang Wei and Jianwei Yang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. P. Degond, “Mathematical modelling of microelectronics semiconductor devices,” in Some Current topics on Nonlinear Conservation Laws, vol. 15 of Proceedings of the Morningside Mathematical Center, Beijing, AMS/IP Studies in Advanced Mathematics, pp. 77–110, AMS Society and International Press, Providence, RI, USA, 2000. View at Google Scholar · View at Zentralblatt MATH
  2. E. Grenier, “Pseudo-differential energy estimates of singular perturbations,” Communications on Pure and Applied Mathematics, vol. 50, no. 9, pp. 821–865, 1997. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  3. S. Wang, “Quasineutral limit of Euler-Poisson system with and without viscosity,” Communications in Partial Differential Equations, vol. 29, no. 3-4, pp. 419–456, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  4. S. Cordier and E. Grenier, “Quasineutral limit of an Euler-Poisson system arising from plasma physics,” Communications in Partial Differential Equations, vol. 25, no. 5-6, pp. 1099–1113, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  5. Y.-J. Peng and Y.-G. Wang, “Convergence of compressible Euler-Poisson equations to incompressible type Euler equations,” Asymptotic Analysis, vol. 41, no. 2, pp. 141–160, 2005. View at Google Scholar · View at Zentralblatt MATH
  6. Y.-J. Peng, Y.-G. Wang, and W.-A. Yong, “Quasi-neutral limit of the non-isentropic Euler-Poisson system,” Proceedings of the Royal Society of Edinburgh A, vol. 136, no. 5, pp. 1013–1026, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  7. Y. Li, “Convergence of the nonisentropic Euler-Poisson equations to incompressible type Euler equations,” Journal of Mathematical Analysis and Applications, vol. 342, no. 2, pp. 1107–1125, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  8. Y. Brenier, “Convergence of the Vlasov-Poisson system to the incompressible Euler equations,” Communications in Partial Differential Equations, vol. 25, no. 3-4, pp. 737–754, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  9. E. Grenier, “Oscillations in quasineutral plasmas,” Communications in Partial Differential Equations, vol. 21, no. 3-4, pp. 363–394, 1996. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  10. N. Masmoudi, “From Vlasov-Poisson system to the incompressible Euler system,” Communications in Partial Differential Equations, vol. 26, no. 9-10, pp. 1913–1928, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  11. I. Gasser, C. D. Levermore, P. A. Markowich, and C. Schmeiser, “The initial time layer problem and the quasineutral limit in the semiconductor drift-diffusion model,” European Journal of Applied Mathematics, vol. 12, no. 4, pp. 497–512, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  12. I. Gasser, L. Hsiao, P. A. Markowich, and S. Wang, “Quasi-neutral limit of a nonlinear drift diffusion model for semiconductors models,” Journal of Mathematical Analysis and Applications, vol. 268, no. 1, pp. 184–199, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  13. Y.-J. Peng and S. Wang, “Convergence of compressible Euler-Maxwell equations to incompressible Euler equations,” Communications in Partial Differential Equations, vol. 33, no. 1–3, pp. 349–376, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  14. Q. Ju, F. Li, and S. Wang, “Convergence of the Navier-Stokes-Poisson system to the incompressible Navier-Stokes equations,” Journal of Mathematical Physics, vol. 49, no. 7, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  15. Q. Ju, F. Li, and H. Li, “The quasineutral limit of compressible Navier-Stokes-Poisson system with heat conductivity and general initial data,” Journal of Differential Equations, vol. 247, no. 1, pp. 203–224, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  16. G. Loeper, “Quasi-neutral limit of the Euler-Poisson and Euler-Monge-Ampère systems,” Communications in Partial Differential Equations, vol. 30, no. 7–9, pp. 1141–1167, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  17. S. Klainerman and A. Majda, “Singular limits of quasilinear hyperbolic systems with large parameters and the incompressible limit of compressible fluids,” Communications on Pure and Applied Mathematics, vol. 34, no. 4, pp. 481–524, 1981. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  18. A. Majda, Compressible Fluid Flow and Systems of Conservation Laws in Several Space Variables, vol. 53, Springer, New York, NY, USA, 1984. View at Publisher · View at Google Scholar