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G. Ali, L. Chen, A. Jüngel, Y. Peng:
"The zero-electron-mass limit in the hydrodynamic model for plasmas";
Nonlinear Analysis: Theory, Methods and Applications, 72 (2010), 4415 - 4427.

The limit of the vanishing ratio of the electron mass to the ion mass in the isentropic
transient Euler-Poisson equations with periodic boundary conditions is proved. The
equations consist of the balance laws for the electron density and current density for
a given ion density, coupled to the Poisson equation for the electrostatic potential. The
limit is related to the low-Mach-number limit of Klainerman and Majda. In particular, the
limit velocity satisfies the incompressible Euler equations with damping. The difference
to the zero-Mach-number limit comes from the electrostatic potential which needs to be
controlled. This is done by a reformulation of the equations in terms of the enthalpy, higherorder
energy estimates and a careful use of the Poisson equation.

Siehe englisches Abstract.

Euler-Poisson system; Incompressible Euler equations; Energy estimates