Geodesic
The Cauchy problem for the two dimensional Euler–Poisson system
Journal of the European Mathematical Society, Tome 16 (2014) no. 10, pp. 2211-2266

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The Euler-Poisson system is a fundamental two-fluid model to describe the dynamics of the plasma consisting of compressible electrons and a uniform ion background. In the 3D case Guo [7] first constructed a global smooth irrotational solution by using the dispersive Klein-Gordon effect. It has been conjectured that same results should hold in the two-dimensional case. In our recent work [13], we proved the existence of a family of smooth solutions by constructing the wave operators for the 2D system. In this work we completely settle the 2D Cauchy problem.
DOI : 10.4171/jems/486
Classification : 35-XX, 00-XX
Keywords: Euler-Poisson, Klein-Gordon, normal form, global well-posedness 
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     title = {The {Cauchy} problem for the two dimensional {Euler{\textendash}Poisson} system},
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Dong Li; Yifei Wu. The Cauchy problem for the two dimensional Euler–Poisson system. Journal of the European Mathematical Society, Tome 16 (2014) no. 10, pp. 2211-2266. doi: 10.4171/jems/486

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