JournalsjemsVol. 16, No. 10pp. 2211–2266

The Cauchy problem for the two dimensional Euler–Poisson system

  • Dong Li

    University of British Columbia, Vancouver, Canada
  • Yifei Wu

    Beijing Normal University, China
The Cauchy problem for the two dimensional Euler–Poisson system cover
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Abstract

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 eff ect. 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.

Cite this article

Dong Li, Yifei Wu, The Cauchy problem for the two dimensional Euler–Poisson system. J. Eur. Math. Soc. 16 (2014), no. 10, pp. 2211–2266

DOI 10.4171/JEMS/486