Convergence of Compressible Euler–Maxwell Equations to Incompressible Euler Equations

In this paper we study the combined quasineutral and non-relativistic limit of compressible Euler–Maxwell equations. For well prepared initial data the convergences of solutions of compressible Euler–Maxwell equations to the solutions of incompressible Euler equations are justified rigorously by an analysis of asymptotic expansions and a careful use of ε-weighted Liapunov-type functional. One main ingredient of establishing uniformly a priori estimates with respect to ε is to use the curl–div decomposition of the gradient.

[1]  F. J. McGrath.  Nonstationary plane flow of viscous and ideal fluids , 1968 .

[2]  Yann Brenier,et al.  Incompressible Euler and E-MHD as scaling limits of the Vlasov-Maxwell system , 2003 .

[3]  P. Degond,et al.  A MODEL HIERARCHY FOR IONOSPHERIC PLASMA MODELING , 2004 .

[4]  Y. Brenier,et al.  convergence of the vlasov-poisson system to the incompressible euler equations , 2000 .

[5]  S. Schochet.  Fast Singular Limits of Hyperbolic PDEs , 1994 .

[6]  Tosio Kato.  Nonstationary flows of viscous and ideal fluids in R3 , 1972 .

[7]  Haim Brezis,et al.  Analyse asymptotique de l'équation de Poisson couplée à la relation de Boltzmann. Quasi-neutralité des plasmas , 1995 .

[8]  A. Majda,et al.  Compressible and incompressible fluids , 1982 .

[9]  Shu Wang,et al.  Quasineutral Limit of Euler–Poisson System with and without Viscosity , 2005 .

[10]  A. Majda,et al.  Singular limits of quasilinear hyperbolic systems with large parameters and the incompressible limit , 1981 .

[11]  Henry Rishbeth,et al.  Introduction to ionospheric physics , 1969 .

[12]  Song Jiang,et al.  The Convergence of the Navier–Stokes–Poisson System to the Incompressible Euler Equations , 2006 .

[13]  Joseph W. Jerome,et al.  Compressible Euler-Maxwell equations , 2000 .

[14]  E. Grenier,et al.  Quasineutral limit of an euler-poisson system arising from plasma physics , 2000 .

[15]  Marshall Slemrod,et al.  Quasi-Neutral Limit for Euler-Poisson System , 2001, J. Nonlinear Sci..

[16]  Yue-Jun Peng,et al.  Convergence of Compressible Euler-Maxwell Equations to Compressible Euler-Poisson Equations* , 2007 .

[17]  Yue-Jun Peng,et al.  Convergence of compressible Euler-Poisson equations to incompressible type Euler equations , 2005 .