References
- Chen F. Introduction to plasma physics and controlled fusion. Vol. 1. New York (NY): Plenum Press; 1984.
- Jerome JW. The Cauchy problem for compressible hydrodynamic-Maxwell systems: a local theory for smooth solutions. Differ. Integral Equ. 2003;16:1345–1368.
- Rishbeth H, Garriott OK. Introduction to ionospheric physics. New York (NY): Academic Press; 1969.
- Brenier Y, Mauser NJ, Puel M. Incompressible Euler and e-MHD as scaling limits of the Vlasov-Maxwell system. Comm. Math. Sci. 2003;1:437–447.
- Yang JW, Wang S, Zhao J. The relaxation-time limit in the compressible Euler-Maxwell equations. Nonlinear Anal. 2011;74:7005–7011.
- Peng YJ, Wang S. Convergence of compressible Euler-Maxwell equations to compressible Euler-Poisson equations. Chin. Ann. Math. 2007;28(B):583–602.
- Wang S. Quasineutral limit of Euler-Poisson system with and without viscosity. Comm. Partial Differ. Equ. 2004;29:419–456.
- Peng YJ, Wang YG, Yong W. Quasi-neutral limit of the non-isentropic Euler-Poisson system. Proc. Roy. Soc. Edinburgh Sect. A. 2006;136:1013–1026.
- Jüngel A, Violet I. The quasineutral limit in the quantum drift-diffusion equations. Asymptot. Anal. 2007;53:139–157.
- Ju QC, Li FC, Li HL. The quasineutral limit of Navier-Stokes-Poisson system with heat conductivity and general initial data. J. Differ. Equ. 2009;247:203–224.
- Feireisl E, Zhang P. Quasi-neutral limit for a model of viscous plasma. Arch. Ration. Mech. Anal. 2010;197:271–295.
- Wu N. Non-relativistic limit of Dirac equations in gravitational field and quantum effects of gravity. Commun. Theor. Phys. 2006;45:452–456.
- Bhattacharyya S, Minwalla S, Wadia SR. The incompressible non-relativistic Navier-Stokes equation from gravity. J. High Energy Phys. 2009;08:059. Available from: http://dx.doi.org/10.1088/1126-6708/2009/08/059
- Stockmeyer E. On the non-relativistic limit of a model in quantum electrodynamics. Preprint, 2009, arXiv:0905.1006v1.
- Alí G, Bini D, Rionero S. Global existence and relaxation limit for smooth solutions to the Euler-Poisson model for semiconductors. SIAM J. Math. Anal. 2000;32:572–87.
- Gasser I, Natalini R. The energy transport the drift diffusion equations as relaxation limits of the hydrodynamic model for semiconductors. Q. Appl. Math. 1999;57:269–282.
- Yong WA. Diffusive relaxation limit of multidimensional isentropic hydrodynamic models for semiconductors. SIAM. J. Appl. Math. 2004;64:1737–1748.
- Li YP. Diffusion relaxation limit of a nonisentropic hydrodynamic model for semiconductors. Math. Methods Appl. Sci. 2007;30:2247–2261.
- Xu J, Yong WA. Relaxation-time limits of non-isentropic hydrodynamic models for semiconductors. J. Differ. Equ. 2009;247:1777–1795.
- Nishibataa S, Suzuki M. Relaxation limit and initial layer to hydrodynamic models for semiconductors. J. Differ. Equ. 2010;249:1385–1409.
- Chen GQ, Jerome JW, Wang DH. Compressible Euler-Maxwell equations. Transp. Theory Stat. Phys. 2000;29:311–331.
- Kato T. Quasilinear equations of evolutions, with applications to partial dierential equation, Lect Notes Math. 1975;448:27–50.
- Yang JW, Wang S. The non-relativistic limit of Euler-Maxwell equations for two-fluid plasma. Nonlinear Anal. 2009;72:1829–1840.
- Yang JW, Wang S. Convergence of the nonisentropic Euler-Maxwell equations to compressible Euler-Poisson equations. J. Math. Phys. 2009;50:123508. doi:10.1063/1.3267863
- Peng YJ, Wang S. Convergence of compressible Euler-Maxwell equations to incompressible Euler equations. Comm. Partial Diff. Eqns. 2008;33:349–476.
- Coulombel JF, Goudon T. The strong relaxation limit of the multidimensional isothermal Euler equations. Trans. Am. Math. Soc. 2007;359:637–648.
- Xu J. Strong relaxation limit of multi-dimensional isentropic Euler equations. Z. Angew. Math. Phys. 2010;61:389–400.
- Marcati P, Natalini R. Weak solutions to a hydrodynamic model for semiconductors and relaxation to the drift-diffusion equations. Arch. Ration. Mech. Anal. 1995;129:129–145.
- Jüngel A, Peng YJ. A hierarchy of hydrodynamic models for plasmas zero-relaxationtime limits. Comm. Partial Differ. Equ. 1999;24:1007–1033.
- Lattanzio C, Marcati P. The relaxation to the drift-diffusion system for the 3-D isentropic Euler-Poisson model for semiconductors. Discrete Contin. Dyn. Syst. 1999;5:449–455.
- Jüngel A, Peng YJ. Zero-relaxation-time limits in hydrodynamic model for plasmas revisited. Z. Angew. Math. Phys. 2000;51:385–396.
- Li Y. Relaxation time limits problem for hydrodynamics models in semiconductor science. Acta Math. Sci. 2007;27B:437–448.
- Yong WA. Singular perturbations of first-order hyperbolic systems with stiff source terms. J. Differ. Equ. 1999;155:89–132.
- Yong WA. Basic aspects of hyperbolic relaxation systems. In: Freistühler H, Szepessy A, editors. Advances in the theory of shock waves. Vol. 47, Progress in nonlinear differential equations and their applications. Boston: Birkhaüser; 2001. p. 259–305.
- Majda A. Compressible fluid flow and systems of conservation laws in several space variables. New York (NY): Springer-Verlag; 1984.
- Klainerman S, Majda A. Singular limits of quasilinear hyperbolic systems with large parameters and the incompressible limit of compressible fluids. Comm. Partial Differ. Equ. 1981;34:481–524.
- Klainerman S, Majda A. Compressible and incompressible fluids. Comm. Pure Appl. Math. 1982;XXXV:629–651.