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Forum Mathematicum

Managing Editor: Bruinier, Jan Hendrik

Ed. by Brüdern, Jörg / Cohen, Frederick R. / Droste, Manfred / Darmon, Henri / Duzaar, Frank / Echterhoff, Siegfried / Gordina, Maria / Neeb, Karl-Hermann / Shahidi, Freydoon / Sogge, Christopher D. / Takayama, Shigeharu / Wienhard, Anna

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Volume 26, Issue 3

Issues

Smooth global solutions for the two-dimensional Euler Poisson system

Juhi Jang / Dong Li / Xiaoyi Zhang
Published Online: 2012-01-13 | DOI: https://doi.org/10.1515/forum-2011-0153

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. By using the dispersive Klein–Gordon effect, Guo (1998) first constructed a global smooth irrotational solution in the three-dimensional case. It has been conjectured that same results should hold in the two-dimensional case. The main difficulty in 2D comes from the slow dispersion of the linear flow and certain nonlocal resonant obstructions in the nonlinearity. In this paper we develop a new method to overcome these difficulties and construct smooth global solutions for the 2D Euler–Poisson system.

Keywords: Euler–Poisson system; 2D; global solution

MSC: 35Qxx

About the article

Received: 2011-12-09

Published Online: 2012-01-13

Published in Print: 2014-05-01


Funding Source: NSF

Award identifier / Grant number: DMS-0908007

Funding Source: NSF

Award identifier / Grant number: 0908032

Funding Source: Alfred P. Sloan fellowship

Funding Source: University of Iowa

Award identifier / Grant number: start-up funding


Citation Information: Forum Mathematicum, Volume 26, Issue 3, Pages 645–701, ISSN (Online) 1435-5337, ISSN (Print) 0933-7741, DOI: https://doi.org/10.1515/forum-2011-0153.

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