Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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Quasineutral limit of the pressureless Euler-Poisson equation for ions


Authors: Xueke Pu and Boling Guo
Journal: Quart. Appl. Math. 74 (2016), 245-273
MSC (2010): Primary 35Q35, 35B25; Secondary 35C20
Published electronically: March 29, 2016
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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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Additional Information

Xueke Pu
Affiliation: Department of Mathematics, Chongqing University, Chongqing 401331, People’s Republic of China
Email: xuekepu@cqu.edu.cn

Boling Guo
Affiliation: Institute of Applied Physics and Computational Mathematics, P.O. Box 8009, Beijing, People’s Republic of China, 100088
Email: gbl@iapcm.ac.cn

DOI: https://doi.org/10.1090/qam/1424
Keywords: Euler-Poisson equation, quasineutral limit, compressible Euler equation
Received by editor(s): August 14, 2014
Published electronically: March 29, 2016
Additional Notes: The first author was supported in part by NSFC (11471057) and Natural Science Foundation Project of CQ CSTC (cstc2014jcyjA50020).
Article copyright: © Copyright 2016 Brown University


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