Quasineutral limit of the pressureless Euler-Poisson equation for ions

Pu, Xueke; Guo, Boling

doi:10.1090/qam/1424

Authors: Xueke Pu and Boling Guo
Journal: Quart. Appl. Math. 74 (2016), 245-273
MSC (2010): Primary 35Q35, 35B25; Secondary 35C20
DOI: https://doi.org/10.1090/qam/1424
Published electronically: March 29, 2016
MathSciNet review: 3505603
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Abstract: In this paper, we consider the quasineutral limit of the Euler-Poisson equation for cold ions when the Debye length tends to zero. In the cold ion case the Euler-Poisson equation is pressureless and hence fails to be Friedrich symmetrizable, excluding the application of the PsDO energy estimates method of Grenier to obtain uniform estimates independent of $\varepsilon$. To overcome this difficulty, we use $\varepsilon$-weighted norms which combine energy estimates in different levels with weights depending on $\varepsilon$. Finally, that the quasineutral regimes are the compressible Euler equations is proven for well prepared initial data. As a natural extension, we also obtain the zero temperature limit of the Euler-Poisson equation.

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