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# The Euler-Maxwell System for Electrons: Global Solutions in 2D

## Author(s): Deng, Yu; Ionescu, Alexandru D; Pausader, Benoit

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 Abstract: A basic model for describing plasma dynamics is given by the Euler-Maxwell system, in which compressible ion and electron fluids interact with their own self-consistent electromagnetic field. In this paper we consider the “one-fluid” Euler-Maxwell model for electrons, in 2 spatial dimensions, and prove global stability of a constant neutral background. In 2 dimensions our global solutions have relatively slow (strictly less than 1/t) pointwise decay and the system has a large (codimension 1) set of quadratic time resonances. The issue in such a situation is to solve the “division problem”. To control the solutions we use a combination of improved energy estimates in the Fourier space, an L (2) bound on an oscillatory integral operator, and Fourier analysis of the Duhamel formula. Publication Date: Aug-2017 Electronic Publication Date: 13-Apr-2017 Citation: Deng, Yu, Ionescu, Alexandru D, Pausader, Benoit. (2017). The Euler-Maxwell System for Electrons: Global Solutions in 2D. ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 225 (771 - 871. doi:10.1007/s00205-017-1114-3 DOI: doi:10.1007/s00205-017-1114-3 ISSN: 0003-9527 EISSN: 1432-0673 Pages: 771 - 871 Type of Material: Journal Article Journal/Proceeding Title: ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS Version: Author's manuscript

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