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The zero-electron-mass limit in the hydrodynamic model for plasmas

✍ Scribed by Giuseppe Alì; Li Chen; Ansgar Jüngel; Yue-Jun Peng

Publisher
Elsevier Science
Year
2010
Tongue
English
Weight
362 KB
Volume
72
Category
Article
ISSN
0362-546X

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✦ Synopsis

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.

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